shear strength and drift capacity of reinforced …
TRANSCRIPT
SHEAR STRENGTH AND DRIFT CAPACITY OF REINFORCED CONCRETE AND HIGH-PERFORMANCE FIBER REINFORCED CONCRETE LOW-RISE
WALLS SUBJECTED TO DISPLACEMENT REVERSALS
by
Adamantia Athanasopoulou
A dissertation submitted in partial fulfillment of the requirements for the degree of
Doctor of Philosophy (Civil Engineering)
in The University of Michigan 2010
Doctoral Committee:
Associate Professor Gustavo J. Parra-Montesinos, Chair Professor Sherif El-Tawil Professor James K. Wight Professor Alan S. Wineman
ii
ACKNOWLEDGEMENTS
This research was possible through the financial support provided by the National
Science Foundation under Grant No. CMS 0324519. The opinions expressed in this
report are those of the writer and do not necessarily reflect the views of the sponsors.
The writer greatly appreciates to have been advised both academically and personally by
Associate Professor Gustavo J. Parra-Montesinos. His invaluable and continuous support
fulfilled the writer’s Ph.D. learning process and was instrumental in the completion of
this dissertation. The writer is also grateful for having the opportunity to be taught by
Professors James K. Wight, Sherif El-Tawil and Alan S. Wineman. The writer wishes to
thank them for their participation in her doctoral committee and for their valuable
comments throughout this research project. Their research enthusiasm and broad
knowledge will definitely inspire and benefit the writer in her professional career.
The author wishes to thank her friends and fellow students at the University of Michigan,
in particular, Hai Dinh, Matt Fadden, Katie Farnum, Peter Heeringa, Terry McGovern,
Heather Munoz, Monthian Setkit, and Elisabeth Windsor for their kind help. Many
special thanks to Remy Lequesne and Min Yuan Cheng for their tremendous help in the
lab and friendship along the way. Sincere thanks are also due to the University of
Michigan Structures Laboratory manager, Jan Pantolin and technicians, Robert Spence
and Robert Fischer, for their invaluable help during the experimental phase of this
research.
Finally, the writer wishes to thank her beloved family, her parents Anastasios and Maria
and her sisters Katerina and Alexia, whose endless love and encouragement were always
with her. The author also wishes to express her gratitude to Kostas for his unconditional
love, support and understanding throughout the course of this research.
iii
TABLE OF CONTENTS
AKNOWLEDGEMENTS ii LIST OF TABLES vi LIST OF FIGURES viii CHAPTER 1 INTRODUCTION 1.1 BACKGROUND AND RESEARCH MOTIVATION 1 1.2 RESEARCH OBJECTIVE AND SCOPE 3 1.3 ORGANIZATION OF THE THESIS 5 CHAPTER 2 LITERATURE REVIEW 2.1 INTRODUCTION 6 2.2 BEHAVIOR OF REINFORCED CONCRETE STRUCTURAL WALLS
2.2.1 General 6 2.2.2 Experimental Research on the Behavior of Low-Rise Reinforced Concrete Structural Walls
2.2.2.1 General Background 8 2.2.2.2 Behavior of Low-Rise Walls under Lateral Loading 9
2.2.3 Design Philosophy and Review of Seismic Design Provisions for Reinforced Concrete Walls in the 2005 ACI Code 18
2.2.4 Estimation of Shear Strength of Low-Rise Reinforced Concrete Structural Walls
2.2.4.1. 2005 ACI Code and Eurocode EC8 23 2.2.4.2 Wood (1990) 26 2.2.4.3 Barda et al. (1977) 27 2.2.4.4 Comments on the Design Equations for Shear Strength of RC Low-Rise Walls 28
2.3 BEHAVIOR AND STRUCTURAL APPLICATIONS OF HIGH-PERFORMANCE FIBER REINFORCED CONCRETE (HPFRC)
2.3.1 Overview and General Characteristics of HPFRC 29 2.3.2 Shear Strength of Fiber Reinforced Cementitious Composite (FRCC) Members 31
2.3.3 Application of HPFRC in Shear-Critical Elements Subjected to Displacement Reversals 33
2.3.4 Application of FRCC Materials in Structural Walls 36 2.4 SUMMARY 38
iv
CHAPTER 3 EXPERIMENTAL PROGRAM 3.1 INTRODUCTION 40 3.2 TEST SPECIMENS
3.2.1 General Description of Test Specimens 41 3.2.2 Design of Test Specimens 42 3.2.3 Reinforcing Details of Test Specimens
3.2.3.1 Specimens with Shear Span-to-Length Ratio of 1.2 47 3.2.3.2 Specimens with Shear Span-to-Length Ratio of 1.5 51
3.3 MATERIALS USED IN THE STUDY 3.3.1 Concrete Mixtures
3.3.1.1 Mixing Proportions 53 3.3.1.2 Mixing Process 55
3.3.2 Fibers 55 3.3.3 Reinforcing Steel 57 3.3.4 Material Testing
3.3.4.1 Concrete and HPFRC Materials 58 3.3.4.2 Reinforcing Steel 59
3.4 CONSTRUCTION OF SPECIMENS 59 3.5 SPECIMENS INSTRUMENTATION 61 3.6 TEST SET UP AND TEST PROCEDURE 62
CHAPTER 4 EXPERIMENTAL RESULTS 4.1 DEFINITIONS
4.1.1 Average Shear Stress 64 4.1.2 Drift 65 4.1.3 Shear Strain 66 4.1.4 Flexural Rotations 67 4.1.5 Horizontal Slip at the Wall Base 68 4.1.6 Calculation of Strain Field from Optotrak Data 68
4.2 DAMAGE PROGRESSION IN THE WALL SPECIMENS 4.2.1 Reinforced Concrete Wall Specimens 70 4.2.2 High-Performance Fiber Reinforced Concrete Wall Specimens 73 4.2.3 Summary of Test Observations 77
4.3 LATERAL LOAD VERSUS DISPLACEMENT RESPONSE 78 4.4 LOAD VERSUS DRIFT ENVELOPE RESPONSE 82 4.5 AVERAGE SHEAR STRAINS 83 4.6 SLIDING SHEAR RESPONSE 86 4.7 HORIZONTAL WALL DILATIONS 89 4.8 ROTATIONS
4.8.1 Concentrated Rotations at the Wall Base 90 4.8.2 Distribution of Rotations along the Wall Height 92
4.9 STEEL STRAINS 93 4.10 STIFFNESS RETENTION CAPACITY 98 4.11 ENERGY DISSIPATION CAPACITY 100
v
CHAPTER 5 ANALYTICAL STUDIES 5.1 DEFORMATION COMPONENTS 102 5.2 CURVATURE
5.2.1 Curvature Distribution 107 5.2.2 Plastic Hinge Length and Curvature Capacity 108 5.2.3 Section Modeling for Prediction of Moment versus Curvature Response 109
5.3 SHEAR FRICTION MODEL 114 5.4 WALL SLIP VERSUS CRACK WIDTH 117 5.5 SHEAR DISTORTION AND ROTATION INTERACTION 117 5.6 SHEAR STRENGTH AND DRIFT CAPACITY OF TEST SPECIMENS AND COMPARISON WITH OTHER STUDIES
119
CHAPTER 6 SUMMARY AND CONCLUSIONS 6.1 SUMMARY 123 6.2 CONCLUSIONS 124 TABLES 130
FIGURES 158
APPENDIX A
285
REFERENCES 293
vi
LIST OF TABLES
Table 2-1 Summary of Tests of Rectangular Low-Rise Reinforced Concrete Structural Walls
130
Table 2-2 Summary of Tests of Barbell and Flanged Low-Rise Reinforced Concrete Structural Walls
134
Table 3-1 Main Features of Test Specimens 135
Table 3-2 Maximum Wall Shear and Calculated Shear Strength of Test Specimens
136
Table 3-3 Nominal Shear Strength for Shear Transfer at the Wall Base of Test Specimens
137
Table 3-4 Extreme Fiber Compressive Stress Corresponding to Maximum Moment for Evaluating Need for Confinement in Boundary Elements According to 2005 ACI Code
137
Table 3-5 Wall Reinforcement Details 138
Table 3-6 Mixture Proportions (by Weight) for Regular Concrete and HPFRC Mixtures
139
Table 3-7 Properties of Fibers 139
Table 3-8 Average Concrete Cylinder Compressive Strength at Test Day (ksi) 140
Table 3-9 ASTM 1609 Beam Test Results 140
Table 3-10 Steel Strength (ksi) 141
Table 4-1 Summary of Test Results 142
Table 4-2 Probable Shear Demand Associated with Flexural Failure and Nominal Shear Strength
143
Table 4-3 Load-Displacement History for Specimen S1 144
Table 4-4 Load-Displacement History for Specimen S2 145
Table 4-5 Load-Displacement History for Specimen S4 146
Table 4-6 Load-Displacement History for Specimen S5 147
Table 4-7 Load-Displacement History for Specimen S6 148
Table 4-8 Load-Displacement History for Specimen S7 149
Table 4-9 Load-Displacement History for Specimen S8 150
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Table 4-10 Load-Displacement History for Specimen S9 151
Table 4-11 Load-Displacement History for Specimen S10 152
Table 4-12 Initial Values for Secant Peak-to-Peak Displacement Stiffness and Corresponding Drifts
153
Table 5-1 Theoretical Yield Curvature Based on Section Modeling 154
Table 5-2 Plastic Hinge Length 154
Table 5-3 Stress-Strain Values for Modeling Concrete (Specimens S4 and S9) and HPFRC (Specimens S5 and S10) Tensile Behavior
154
Table 5-4 Compressive Stress-Strain Model for Regular Concrete (Specimens S4 and S9) and HPFRC (Specimens S5 and S10) Matrix
155
Table 5-5 Compressive Strains at Wall Edges in RC Specimens (Specimen S4 and S9)
155
Table 5-6 Friction Coefficient Values Based on Test Results 156
Table 5-7 Elastic Sliding Stiffness Normalized by Shear Friction Strength, (µ = 1)
156
Table 5-8 Comparison of Test Results with Other Studies 157
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LIST OF FIGURES
Fig. 1-1 Typical Reinforcement Detailing in the Boundary Regions of Reinforced Concrete Structural Walls
158
Fig. 2-1 Shear Failure Modes in RC Low-Rise Structural Walls (Paulay et al., 1982)
159
Fig. 2-2 Development of Sliding Shear Mechanism in RC Low-Rise Walls (Pauley et al., 1982)
160
Fig. 2-3 Reinforcing Detailing for the Wall Specimens Tested by Cardenas et al. (1980)
161
Fig. 2-4 Low-Rise Wall Specimen Details in the Study by Paulay et al. (1982) 162
Fig. 2-5 Geometry of Test Specimens by Wiradinata and Saatcioglu (1986) 162
Fig. 2-6 Reinforcement Layout in the Wall Specimens Tested by Sittupint et al. (2001)
163
Fig. 2-7 Test Set-Up for Low-Rise Wall Specimens used by Hidalgo et al. (2002)
163
Fig. 2-8 Wall Test Set-Up by Lopes (2000 (a) 164 )
Fig. 2-9 Tensile Stress-Strain Behavior of HPFRCCs (Naaman, 1998) 164
Fig. 2-10 Coupling Beam Specimens in the Study by Canbolat et al. (2005) 165
Fig. 3-1 Dimensions of Test Specimens 166
Fig. 3-2 Reinforcement Details for Bottom and Top Block in Specimens S1, S2, S6, S7 and S8
167
Fig. 3-3 Reinforcement Details for Bottom and Top Block in Specimens S4, S5, S9 and S10
168
Fig. 3-4 Reinforcement Layout in Specimen S1 169
Fig. 3-5 Reinforcement Layout in Specimen S2 170
Fig. 3-6 Reinforcement Layout in Specimen S4 171
Fig. 3-7 Dowel Reinforcement in Specimen S5 172
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Fig. 3-8 Sleeves in Dowel Reinforcement (Specimen S10) 172
Fig. 3-9 Reinforcement Layout in Specimen S5 173
Fig. 3-10 Reinforcement Layout in Specimen S6 174
Fig. 3-11 Reinforcement Layout in Specimens S7 and S8 175
Fig. 3-12 Reinforcement Layout in Specimen S9 176
Fig. 3-13 Reinforcement Layout in Specimen S10 177
Fig. 3-14 Laboratory Concrete Mixers 178
Fig. 3-15 Fibers Used in this Study (Naaman, 1999) 178
Fig. 3-16 Wire Used in Specimens S4, S5, S9 and S10 179
Fig. 3-17 ASTM 1609 Beam Test Set-Up 179
Fig. 3-18 Load versus Deflection Response for ASTM 1609 Beam Specimens (Specimen S5)
180
Fig. 3-19 Load versus Deflection Response for ASTM 1609 Beam Specimens (Specimen S10)
180
Fig. 3-20 Tensile Stress versus Strain Response for D4 Crimped Wire (Three Coupons)
181
Fig. 3-21 Base Block inside Formwork (Specimen S4) 181
Fig. 3-22 Base Block Ready for Casting (Specimen S10) 182
Fig. 3-23 Elevation View of Wall Reinforcement Layout (Specimen S10) 182
Fig. 3-24 Wall Ready for Casting (Specimen S10) 183
Fig. 3-25 Bottom Beam and Wall after Removal of Formwork (Specimen S4) 183
Fig. 3-26 View of Top Beam inside Formwork (Specimen S9) 184
Fig. 3-27 Completed Specimen (Specimen S6) 184
Fig. 3-28 Instrumentation Scheme for Specimens with Shear Span-to-Length Ratio of 1.2
185
Fig. 3-29 Instrumentation Scheme for Specimens with Shear Span-to-Length Ratio of 1.5
186
Fig. 3-30 Optotrak System Markers Grid 187
Fig. 3-31 Instrumentation Scheme with Potentiometers and Clinometers 188
Fig. 3-32 Optotrak Instrumentation Scheme 188
Fig. 3-33 Lateral Bracing Scheme (Specimen S10) 189
Fig. 3-34 Specimen S4 before Testing 189
Fig. 3-35 Test Set-Up for Specimen S9 190
Fig. 3-36 Lateral Displacement History 191
x
Fig. 4-1 Calculation of Wall Lateral Displacement 192
Fig. 4-2 Lateral Force versus Top-Block Displacement Envelope for Specimen S5 192
Fig. 4-3 Calculation of Shear Strain (adapted from Sittipunt and Wood, 1995) 193
Fig. 4-4 Definition of “Longitudinal Strips” in Wall Specimen 193
Fig. 4-5 Deformation of a Quadrilateral Element for Calculation of Average Strains 194
Fig. 4-6 Cracking Pattern in Specimen S1 195
Fig. 4-7 Cracking Pattern in Specimen S4 196
Fig. 4-8 Cracking Pattern in Specimen S6 198
Fig. 4-9 Cracking Pattern in Specimen S9 199
Fig. 4-10 Cracking Pattern in Specimen S2 201
Fig. 4-11 Cracking Pattern in Specimen S5 203
Fig. 4-12 Cracking Pattern in Specimen S7 205
Fig. 4-13 Cracking Pattern in Specimen S8 206
Fig. 4-14 Cracking Pattern in Specimen S10 207
Fig. 4-15 Load versus Drift Response 209
Fig. 4-16 Comparison of Shear Stress versus Drift Response for Specimens S9 and S10
213
Fig. 4-17 Load versus Drift Envelope Response 214
Fig. 4-18 Load versus Average Shear Strain Response 219
Fig. 4-19 Comparison of Shear Strain Response Calculated using Diagonal Potentiometers and Optotrak Markers (Specimen 5)
223
Fig. 4-20 Average Shear Strain versus Drift Envelope Response 224
Fig. 4-21 Comparison of Shear Strain Response Calculated Using Method 1 (Eq. 4-4) and Method 2 (average of shear strain in the longitudinal strips) (Specimen S4)
225
Fig. 4-22 Shear Strain versus Drift Envelope Response at Each Strip (Specimen S10) 226
Fig. 4-23 Load versus Base Slips Response for RC Specimens 227
Fig. 4-24 Load versus Base Slip Response for HPFRC Specimen S2 229
Fig. 4-25 Load versus Slip Response at Horizotnral Crack for HPFRC Specimens with Dowel Bars at the Base
229
Fig. 4-26 Load versus Dilation Response for Specimens with a Shear Span-to-Length Ratio of 1.5
230
Fig. 4-27 Comparison of Dilation at Bottom of Wall for Specimens S9 and S10 232
Fig. 4-28 Load versus Concentrated Rotation for Test Specimens 232
xi
Fig. 4-29 Rotation versus Drift Envelope Response for Wall Specimens 237
Fig. 4-30 Load versus Strain Response in Longitudinal Bars of Wall Boundary Element in Specimen S1
241
Fig. 4-31 Load versus Strain Response in a Horizontal Bar of Specimen S1 242
Fig. 4-32 Load versus Strain Response in a Vertical Bar of Specimen S4 242
Fig. 4-33 Load versus Strain Response in a Horizontal Bar of Specimens S4 and S5 243
Fig. 4-34 Load versus Strain Response in Longitudinal Bar of Wall Boundary Element in Specimen S6
243
Fig. 4-35 Load versus Strain Response in Horizontal Bars of Specimen S6 244
Fig. 4-36 Load versus Strain Response in Horizontal Bars at 0.3h for Specimens S9 and S10
244
Fig. 4-37 Drift versus Strain in Main Longitudinal Bars at 1 in. from Wall Base 245
Fig. 4-38 Drift versus Strain in Main Longitudinal Bars at Wall Mid-Height 246
Fig. 4-39 Drift versus Strain in Dowel Bars at 1 in. from Wall Base in the HPFRC Specimens
247
Fig. 4-40 Drift versus Strain at a Horizontal Bar at a Height of 0.1h 247
Fig. 4-41 Drift versus Strain at a Horizontal Bar at a Height of 0.25h 248
Fig. 4-42 Drift versus Strain at a Horizontal Bar at Height of 0.5h 249
Fig. 4-43 Normalized Peak-to Peak Stiffness versus Drift for Wall Specimens 250
Fig. 4-44 Comparison of Normalized Stiffness for RC Wall Specimens 252
Fig. 4-45 Comparison of Normalized Stiffness for HPFRC Wall Specimens 252
Fig. 4-46 Energy Dissipated versus Drift for Wall Specimens 253
Fig. 4-47 Normalized Energy Dissipated versus Drift for Wall Specimens 254
Fig. 5-1 Definition of Shear Strain for the Calculation of Wall Deformation Components
255
Fig. 5-2 Calculation of Curvature over the Wall Height 256
Fig. 5-3 Contribution of Deformation Components to Drift 257
Fig. 5-4 Curvature Distribution for RC Specimen S4 259
Fig. 5-5 Curvature Distribution for HPFRC Specimen S5 260
Fig. 5-6 Curvature Distribution for RC Specimen S9 262
Fig. 5-7 Curvature Distribution for HPFRC Specimen S10 264
Fig. 5-8 Tensile Stress-Strain Model for HPFRC Matrix 266
Fig. 5-9 Compression Stress-Strain Model for Regular Concrete and HPFRC Matrix
266
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Fig. 5-10 Tensile Stress-Strain Model for Steel Reinforcement 267
Fig. 5-11 Moment versus Curvature Response for RC Specimen S4 268
Fig. 5-12 Moment versus Curvature Response for HPFRC Specimen S5 269
Fig. 5-13 Moment versus Curvature Response for RC Specimen S9 270
Fig. 5-14 Moment versus Curvature Response for HPFRC Specimen S10 271
Fig. 5-15 Ratio of Measured Shear Strength to Shear Strength Calculated Using the Shear Friction Analogy versus Shear Friction Strength
272
Fig. 5-16 Measured Shear Strength versus Shear Friction Capacity 272
Fig. 5-17 Measured Normalized Shear Strength versus Shear Friction Strength
273
Fig. 5-18 Shear Force Normalized by Shear Friction Strength versus Horizontal Sliding Envelope Response
273
Fig. 5-19 Shear Force Normalized by Shear Friction Strength versus Horizontal Sliding Envelope Response for HPFRC Specimens S5 and S10 at the Wall Base (Cold Joint)
274
Fig. 5-20 Sliding Stiffness versus Average Horizontal Crack Width 275
Fig. 5-21 Sliding Stiffness Normalized by Shear Friction Capacity versus Average Horizontal Crack Width
275
Fig. 5-22 Sliding Stiffness and Slip versus Crack Width on Tension Face of Horizontal Crack for HPFRC Specimen S5
276
Fig. 5-23 Sliding Stiffness and Slip versus Crack Width on Tension Face of Horizontal Crack for HPFRC Specimen S10
278
Fig. 5-24 Shear Stress versus Shear Distortion in HPFRC Specimens S7 and S8 280
Fig. 5-25 Shear Strain to Rotation Ration versus Shear Stress for Specimens S7 and S8
281
Fig. 5-26 Peak Shear Stress versus Drift Capacity for Test Specimens in this Study 282
Fig. 5-27 Comparison of Peak Shear Stress versus Drift Capacity for Walls with No or Little Confinement Reinforcement in the Boundary Region
283
Fig. 5-28 Peak Shear Stress versus Drift Capacity for Wall Specimens with Various Confinement Reinforcing Ration
284
1
CHAPTER 1
INTRODUCTION
1.1 BACKGROUND AND RESEARCH MOTIVATION
Since the 1960s, considerable research, as well as lessons learned from previous
earthquakes, have led to improved understanding of the seismic behavior of structural
walls. Among the first reported observations concerning the seismic behavior of
structural walls were those after the Chilean earthquake of 1960, as reported in the
Advance Engineering Bulletin No. 6 issued by the Portland Cement Association, where
the efficiency of structural walls in controlling structural damage during severe
earthquakes was noted. In the early 1970s, Fintel (1974) indicated that properly designed
structural walls could be used effectively as the primary lateral-load resisting system for
both wind and earthquake loading in multistory buildings. Structural wall systems have
also been recognized as a favorable alternative to ductile moment-resistant frames
(Sittipunt et al., 2001). Today, reinforced concrete structural walls are frequently used as
the primary component of the lateral load-resisting system in buildings located in
earthquake-prone regions because of their substantial contribution to building lateral
strength and stiffness.
The seismic design of reinforced concrete structural walls in the U.S. follows the
provisions of Chapter 21 of the ACI Building Code (ACI Committee 318, 2008). These
are perhaps the most widely used provisions for the design of structural walls located in
earthquake-prone regions. Typical reinforcement requirements for structural walls,
besides flexural reinforcement, include distributed vertical and horizontal reinforcement
in the web of the wall. Special confinement reinforcement at the wall edges, in the form
2
of closely spaced hoops, is often required to avoid early concrete crushing when the
expected compression strain and/or stress demand is large. Fig. 1-1 shows the typical
reinforcement detailing in the boundary regions of RC structural walls.
Low-rise walls are typically defined as those having a height-to-length ratio smaller than
two and thus, they exhibit a behavior highly influenced by shear. Low-rise walls can be
found in low-rise buildings such as parking structures, and in high-rise structures, when
the walls extend only a few stories above the foundation level (Pauley et al., 1981). The
required seismic detailing of low-rise structural walls, even though it is believed to lead
to an acceptable level of performance, can translate into severe reinforcement congestion
and construction difficulties. In addition, experimental studies focusing on the behavior
of reinforced concrete low-rise walls have generally revealed limited drift capacity, in
some cases as low as 0.3% (Barda et al., 1977; Pauley et al., 1981; Hidalgo et al., 2002).
Thus, there is room for improvements in performance and possibly, for simplifications in
reinforcement detailing.
A design alternative that could lead to enhanced seismic behavior while allowing for
simplifications in reinforcement detailing in low-rise walls is the use of discontinuous,
randomly oriented steel fibers added to the concrete. Fiber reinforcement can be very
effective for bridging cracks in any direction because of the random orientation of the
fibers. Also, the use of fiber reinforcement often leads to a reduced crack spacing with
the associated narrower crack widths and increase in shear strength and damage
tolerance. Of particular interest for use in low-rise wall construction is High-Performance
Fiber Reinforced Concrete (HPFRC), which is a new type of fiber reinforced concrete
that exhibits a strain-hardening behavior under direct tension. This material has been used
in shear-critical elements with very promising results in terms of shear resistance,
deformation capacity and damage tolerance (Parra, 2005).
3
Kim and Parra (2003) proposed the use of HPFRC in lieu of regular concrete in low-rise
walls. A pilot experimental study that consisted of the testing of two HPFRC low-rise
walls under displacement reversals showed that the use of an HPFRC material offers the
potential for a significant relaxation in the required web and confinement reinforcement
while enhancing wall displacement capacity and damage tolerance.
To the writer’s knowledge, no work other than the pilot study by Kim and Parra (2003)
has been conducted on the behavior of HPFRC low-rise structural walls under
displacement reversals. Thus, prior to this study, very limited information was available
on the shear strength and deformation capacity of HPFRC walls subjected to reversed
cyclic loading. Based on the encouraging results from the pilot study by Kim and Parra
(2003), a comprehensive experimental and analytical research project was therefore
undertaken to evaluate in depth the seismic behavior of HPFRC low-rise walls and to
develop analytical tools for their modeling and design.
1.2 RESEARCH OBJECTIVE AND SCOPE
The main objective of this research was to evaluate the potential of using HPFRC
materials in low-rise walls in order to simplify transverse reinforcement detailing while
enhancing shear resistance, deformation capacity and damage tolerance when subjected
to earthquake-induced lateral displacements.
The scope of this thesis was limited to rectangular cantilever low-rise walls constructed
with either regular concrete or an HPFRC material. Two shear span-to-length ratios were
evaluated, 1.2 and 1.5, and no axial load was applied to the walls. The HPFRCs used
contained either steel or ultra-high molecular weight polyethylene (Spectra) fibers in
volume fractions between 1.5% and 2.0%.
In order to achieve the research objective, the following tasks were performed:
4
The review of the relevant literature covered two basic topics. The first topic focused on
the behavior and design of reinforced concrete walls under lateral loading. In particular,
previous experimental studies on reinforced concrete low-rise walls were reviewed so
that the parameters that influence wall shear strength and deformation capacity could be
identified. This review was followed by a presentation of the design philosophy for
reinforced concrete structural walls with emphasis on the seismic provisions of the 2005
ACI Code (ACI Committee 318, 2005). The second review topic focused on the behavior
of HPFRC materials and their application in shear-critical elements, with emphasis on
existing methods for estimating the shear strength of fiber-reinforced concrete members
under monotonic and reversed cyclic loading.
Task 1: Literature Review
The experimental program included the design and testing of seven low-rise walls under
reversed cyclic displacements. Four specimens were constructed with regular concrete,
which were designed according to the seismic provisions (Chapter 21) of the 2005 ACI
Code (ACI Committee 318, 2005). The use of an HPFRC material in combination with a
simplified reinforcing detailing was evaluated through the testing of HPFRC low-rise
wall specimens under approximately the same shear stress level as their companion RC
walls. The main experimental parameters were: 1) average shear stress level; 2) wall
height-to-length ratio; 3) web and tension reinforcement ratio; 4) use of fiber reinforced
concrete versus fiber reinforced mortar, and 5) effect of addition of dowel bars at the
wall-foundation interface for HPFRC walls.
Task 2: Experimental Studies
The evaluation of the experimental behavior of the RC and HPFRC test walls was mainly
based on the load versus displacement hysteresis response, sliding shear response,
rotations along the wall height, shear distortions, and energy dissipation capacity.
Emphasis was also given to the identification of the different deformation mechanisms
Task 3: Experimental Results and Analytical Studies
5
and their contribution to overall drift, so that conclusions could be drawn about the
modeling of low-rise walls. In this part of the study, the test results reported by Kim and
Parra (2003) from the pilot study on HPFRC low-rise walls were further analyzed and
included in the analytical program.
The final task consisted of a summary of the main aspects of the research program and
conclusions drawn from the experimental and analytical studies.
Task 4: Summary and Conclusions
1.3 ORGANIZATION OF THE THESIS
This report is organized in six chapters. In the first chapter a brief introduction to the
research project is given, followed by a statement of the research objective and scope. A
review of relevant research work on the behavior of RC low-rise walls and structural
applications of HPFRC materials is presented in Chapter 2. Chapter 3 focuses on the
experimental program, where the reinforcing details of the specimens, the materials used,
the test protocol, and other testing issues are discussed. Chapter 4 presents the basic
experimental results, whereas Chapter 5 focuses on the analytical studies and in-depth
discussion of the behavior of the test specimens. Conclusions and recommendations
drawn from this study are provided in Chapter 6.
6
CHAPTER 2
LITERATURE REVIEW
2.1 INTRODUCTION
In this chapter, a literature review on topics related to this research study is presented. A
short review on the behavior and design of low-rise reinforced concrete structural walls is
presented in Section 2.2. Emphasis is given on experimental investigations on isolated
low-rise walls with similar characteristics to those of the specimens tested in this study. A
review of the 2005 ACI Code seismic provisions (ACI Committee 318, 2005) for low-
rise shear walls is then followed by a discussion of predictive equations for the shear
strength of structural walls. Section 2.3 provides an overview of the behavior and
characteristics of High-Performance Fiber Reinforced Concrete (HPFRC) materials and a
discussion of their structural applications on shear-critical members subjected to
displacement reversals.
2.2 BEHAVIOR OF REINFORCED CONCRETE STRUCTURAL WALLS
2.2.1 General
Reinforced concrete structural walls are deep and relatively thin, vertical cantilever
members, also referred to as “shear walls”. Structural walls are widely used in reinforced
concrete buildings located in earthquake-prone regions as the primary lateral-load
resisting mechanism, because of their efficiency to provide lateral strength and stiffness,
and control the lateral drift. Structural walls can also be an effective solution to
rehabilitate deficient existing structures. As documented by several researchers (for
example Fintel, 1991; Wood, 1991), buildings with reinforced concrete walls have shown
good performance during recent earthquakes, which has made structural concrete walls a
7
quite popular alternative to reinforced concrete frames in regions of high seismicity, such
as the west coast of the U.S., New Zealand, Chile, among others.
Structural walls can be found in various shapes and sizes, with different configurations in
the building plan. Symmetrical sections, for example rectangular and barbell shaped, are
quite frequent, although “flanged”, asymmetrical wall sections such as T- and L-shaped
sections are also often used. The effect of the wall cross-section shape on the seismic
behavior of a shear wall has been investigated by several researchers and it has been
shown that the wall strength, stiffness, and ductility depend greatly on the shape of the
wall (Paulay, 1986(a)
; Wallace and Moehle, 1989).
One of the most common classifications of structural walls is with respect to their overall
height-to-length ratio (wall aspect ratio, ). Walls with aspect ratio greater than two
are usually referred to as “slender walls” and have a behavior mainly dominated by
flexure. Slender walls are quite common in tall buildings because of their efficiency in
resisting lateral loads and limiting lateral drift. Structural walls with an aspect ratio
smaller than two are usually called “low-rise” walls, where shear tends to govern the
overall wall response. “Squat walls” are typically defined as walls with an aspect ratio
smaller than one. Low-rise walls find application in residential buildings, parking
structures, industrial buildings, nuclear power plants, and also in highway overpasses and
bridge abutments. Furthermore, low shear span-to-length ratios (shear aspect ratio, )
can be found in slender walls at the basement of high-rise structures if the magnitude of
the bending moment at the foundation level is significantly reduced from its maximum
value, at the top of the basement (Salonikios, 2007).
Since the 1960s, several research projects have focused on the behavior of slender and
low-rise walls under monotonic and reversed lateral cyclic loading. Based on
experimental investigations, factors that affect the behavior of structural walls, especially
their deformation capacity, include the wall aspect ratio and configuration, axial load,
8
shear stress demand, and wall reinforcement ratios (Wallace and Moehle, 1992; Wallace,
1994; 1995(a); 1995(b)
). The philosophy often used in the design of concrete walls focuses
on providing the required strength and stiffness to avoid or limit damage under frequent
earthquakes (limited or no inelastic behavior) while ensuring sufficient wall deformation
capacity so that the lateral load capacity can be maintained during the inelastic response
expected during stronger, less frequent earthquakes (Massone and Wallace, 2004).
Structural walls must also be able to dissipate energy after yielding to survive strong
ground motions, as noted by Pauley et al. (1982), and should not be susceptible to sudden
failures due to shear or local instabilities.
The ultimate shear strength of shear walls and the design criteria to adequately resist
shear has been the focus of many experimental and analytical studies (Hidalgo et al.,
2002). Two different approaches have been used by researchers for predicting the
ultimate shear strength of shear walls: the derivation of empirical expressions based on
test results (for example Barda et al., 1977; Aktan and Bertero, 1985; Wood, 1989;
Wood, 1990), and the application of shear models based on structural mechanics through
the use of equilibrium, compatibility and material constitutive relationships (for example
Collins and Mitchell, 1986; Aoyama, 1991). Most of the seismic design provisions found
in modern building codes, such as the ACI Code provisions (ACI Committee 318, 2008),
use empirical or semi-empirical equations to estimate the ultimate shear strength of shear
walls.
2.2.2 Experimental Research on the Behavior of Low-Rise Reinforced Concrete
Structural Walls
2.2.2.1. General Background
Before the 1970s, experimental research on reinforced concrete structures was primarily
directed towards the understanding of the behavior of moment resisting frames. Limited
work was reported on the behavior of structural walls under earthquake-type loading
(Lopes, 2001(b)). Benjamin and Williams (1957; 1958; 1960) conducted one of the
9
earliest experimental investigations on the behavior and strength of one-story plain and
reinforced concrete structural walls. Later, in 1968, the U.S. Portland Cement Association
(PCA) undertook an extensive test program in order to generate information on the
behavior and strength characteristics of structural walls for high and low-rise buildings
(Cardenas et al., 1973; 1980; Oesterle et al., 1976; 1979).
After the 1970s, the interest on the seismic behavior of isolated and coupled structural
walls grew. Fintel (1991) documented the superiority of structural walls to resist lateral
forces induced by seismic excitations and several experimental investigations focusing on
structural walls were carried out in the U.S., Europe, New Zealand, and Japan. In
particular, the remarkably good performance of structural wall dominant buildings during
the 1985 Chilean earthquake inspired an increase in the amount of research on the
seismic behavior and detailing requirements of reinforced concrete walls in the U.S.
(Thomsen and Wallace, 1995).
2.2.2.2 Behavior of Low-Rise Walls under Lateral Loading
The behavior of low-rise walls may be quite different from that of slender walls because
of the effect of the wall aspect ratio (deep member behavior versus beam-type behavior
for low-rise and slender walls, respectively). Typical failure modes observed in low-rise
walls subjected to lateral loading (monotonic or cyclic) are well documented and include:
diagonal tension failure, diagonal compression failure (or web crushing and/or splitting
failure), and sliding shear failure at the base of the wall (Pauley et al., 1982). Fig. 2-1
schematically presents the diagonal tension and diagonal compression failure modes. A
typical corner-to-corner diagonal tension failure is shown in Fig. 2-1(a) whereas Fig. 2-
1(b) illustrates a case where a steeper diagonal crack leads to failure. Figs. 2-1(c) and (d),
on the other hand, present a diagonal compression and a web crushing failure under
monotonic and cyclic loading, respectively.
10
The development of a ductile flexural response is generally favorable since failures due
to shear can lead to limited ductility and premature degradation in stiffness and strength.
Shear failure should thus be avoided in seismic design. Diagonal tension failure can be
avoided by providing sufficient horizontal and vertical shear reinforcement, whereas
limitations in the wall flexural strength (and thus in shear stress demand) can insure that a
diagonal compression failure mechanism will not govern. Oesterle et al. (1984) suggested
that low-rise walls are more susceptible to web crushing prior to flexural yielding
compared with slender walls. It is also possible that in cases of high axial compression
and flexure in rectangular walls, the boundary zone under compression may fail through
out-of-plane instability (Aktan and Bertero, 1985). Furthermore, walls that are lightly
reinforced are also prone to failure by fracture of the reinforcement, particularly in cases
where axial tension can be developed by the foundation system, as reported by Wood
(1989).
Even though diagonal tension and compression failure mechanisms can be avoided, a
significant reduction in stiffness and a consequent reduction in the energy dissipation
capacity of the wall could occur because of sliding shear deformations. The start of the
mechanism of sliding shear is illustrated in Figure 2-2(a), as reported by Paulay et al.
(1982). At this stage, the shear force is primarily transmitted at the wall base across the
uncracked flexural compression zone. Typically, sliding shear deformations are observed
after significant flexural yielding has occurred during load reversals and flexural cracks
connect to form a continuous horizontal crack along a deteriorated cracked region at or
near the base (Pauley et al., 1982), as shown in Fig. 2-2(b). At this point, the wall may
rotate as a rigid body and because of the progressive yielding, when the load is reversed,
sliding displacement occurs along the horizontal crack. Fig. 2-3(c) illustrates the
transmission of flexural compression stresses after yielding of the compression steel,
which allows closing of the horizontal crack at the compression end of the wall. Prior to
sliding shear failure, shear is transferred primarily by “dowel action because of the
significant deterioration of the shear friction mechanism along the plane of the sliding
shear deformations.
11
Sliding shear deformations can be significant for walls with increased shear demand or
with low axial compression force, as noted by Pauley et al. (1982). Corley et al. (1981)
reported that damage by sliding shear is anticipated in the range of nominal shear stresses
from approximately to (psi), where is the concrete cylinder compression
strength in psi. In the same study by Corley et al., it was reported that when the shear
stress demand exceeds (psi), the formation of a concrete diagonal strut may
preclude the development of a sliding shear failure mechanism.
Barda et al. (1977) investigated the behavior of six cantilever structural wall specimens
with shear span-to-length ratios, , ranging from 0.25 to 1.0. All the specimens had a
flanged cross-section and boundary elements with transverse reinforcement. Two of the
specimens were subjected to load reversals, whereas the rest of the tests were conducted
under monotonic loading. The specimens were tested under a high level of shear stress,
ranging from to (psi). Very limited drift capacities were reported at failure
(less than 1.0%), in addition to a significant loss of stiffness and strength after the peak
load. Based on the test results it was concluded that horizontal reinforcement was
ineffective for shear resistance in walls with shear span-to-length ratios less than 0.5.
Vertical reinforcement was found to be mostly effective for walls with shear span-to-
length ratios between 0.25 and 0.5 and less effective for walls with a ratio of 1.0.
However, the research results clearly indicated that minimum horizontal and vertical web
reinforcement should be provided in all walls regardless of their aspect ratio because it
results in more evenly distributed cracks with reduced widths. It was also pointed out that
a significant portion of shear introduced at the top of the wall is transmitted directly to the
foundation by diagonal compression. The authors also reported in the same study that the
shear strength of the specimen with a shear aspect ratio of 1.0 was about 20% lower than
that of the specimens with smaller aspect ratios (i.e. ratios of 0.25 and 0.5), verifying the
advantageous effect of a low wall shear span-to-length ratio on the shear strength of
structural walls.
12
Cardenas et al. (1980) reported on the results of seven rectangular reinforced concrete
walls with a shear span-to-length ratio of 1.1 and no special boundary elements. The
reinforcing detailing of the specimens is shown in Fig. 2-3. Only one specimen was
subjected to cyclic loading, whereas the other walls were tested under monotonic lateral
loading. Major parameters in the study were the amount and distribution of the vertical
and horizontal reinforcement. It was concluded that both the vertical and horizontal
reinforcement contribute to the shear strength of low-rise walls, but their relative
effectiveness was not studied further. The authors reported drifts at failure in the range of
0.6% to 1.9% for the wall tested under monotonic loading, whereas the specimen
subjected to cyclic loading failed at a drift of approximately 0.5%. An upper limit in the
order of (psi) was proposed for the shear strength of low-rise walls. It should be
noted that the authors defined the average shear stress based on the effective depth of the
section, , rather than the length of the wall, , which is used in the 2005 ACI Code.
Synge (1980) and Pauley et al. (1982) addressed the issue of ductility and sliding shear
deformations in low-rise walls. The study was based on the response of four walls with a
shear span-to-length ratio of 0.6, tested under reversed cyclic loading. The walls had
either a rectangular or a flanged cross section and were reinforced with an orthogonal
grid of web reinforcement. Bi-diagonal web reinforcement, as shown in Fig. 2-4, was
added in two specimens to evaluate its effectiveness in resisting sliding shear. Transverse
reinforcement in the wall boundary regions was provided to prevent premature buckling
of the longitudinal reinforcement. Maximum shear stresses for the specimens were in the
range of to (psi). It was reported that the rectangular wall specimen
reinforced with an orthogonal grid of web reinforcement exhibited a substantial loss of
strength in the second cycle to a drift of 0.6%, when sliding deformations became
significant (approximately 65% of the applied lateral displacement). In the wall specimen
with a flanged section and orthogonal grid of web reinforcement, excessive sliding and
loss of stiffness was observed when 0.35% drift was reached, leading to an overall
inferior performance in terms of energy dissipation capacity compared with the wall with
rectangular cross section. An enhanced response in terms of energy dissipation and
13
improved control of sliding shear deformations was observed in the specimens where
diagonal reinforcement was used. Strength loss was reported in the diagonally reinforced
rectangular specimen during the second cycle to a drift of 0.8% while buckling of the
diagonal bars was observed at 1.3% drift. The flanged wall specimen with diagonal
reinforcement maintained its strength up to a drift of 0.4% and exhibited a more gradual
loss of strength compared with the flanged specimen without diagonal reinforcement.
Buckling of the diagonal bars in this specimen was reported at a drift of 1.5%.
Wiradinata and Saatcioglu (1986) tested two reinforced concrete walls with rectangular
cross-section and a shear span-to-length ratio of 0.3 and 0.6. Fig. 2-5 shows the
dimensions of the two specimens. The taller wall reached a peak shear stress of about
(psi) and failed by diagonal tension at a drift of 1.7%. The specimen with a shear
aspect-to-length ratio of 0.3 exhibited a highly pinched hysteretic behavior that was
attributed to excessive sliding deformations at the base of the wall, which contributed
more than 70% to the lateral displacement at the end of the test. In the specimen with a
shear span-to-length ratio of 0.6, even though flexural and shear deformations were both
significant throughout the test, shear deformations clearly governed once the wall
strength started to degrade. Based on the limited test results, the authors concluded that
walls with a shear span-to-length ratio of approximately 0.3 are more susceptible to
sliding shear failures compared to more slender walls. It should be noted, however, that
even though the shorter wall could not develop its flexural strength prior to a sliding
shear failure, the reported drift at failure was surprisingly high (2.6%). No discussion was
provided by the authors though. The test results also confirmed the observation made by
other researchers that vertical reinforcement is highly effective in resisting shear in squat
walls.
Lefas et al. (1990) studied the strength, deformation characteristics and failure
mechanism of wall specimens with a shear span-to-length ratio of 1.1 and 2.1. All the
specimens had a rectangular cross-section with transverse reinforcement in the boundary
elements. In terms of wall strength, the advantageous arching effect with a decreasing
14
shear aspect ratio was verified by the test results. The walls with a shear span-to-length
ratio of 1.1 sustained shear stresses in the range of to (psi), while
maximum shear stresses of to (psi) were measured in the group of
specimens with a shear span-to-length ratio of 2.1. Drifts at failure ranged from about
1.0% to 1.5%, the specimens with a shear span-to-length ratio of 2.1 reaching the larger
drifts. All the specimens were reported to fail due a nearly vertical splitting of the
compressive zone close to the wall base, with a more extensive failure region for the
lower aspect ratio walls and the specimens that were subjected to axial load. The authors
discussed the effectiveness of the compression zone as a shear transfer mechanism at the
wall base, and concluded that it is associated with the development of triaxial
compressive stress conditions near the base of the wall, suggesting that the horizontal
web reinforcement and the aggregate interlock did not significantly affect the load-
capacity of the walls tested.
Tests on structural walls with a shear span-to-length ratio of 1.2 were reported by Maier
(1992). Main parameters in the tests were the wall cross section (rectangular or barbell
shape), the effect of boundary elements, and the type of loading (monotonic or cyclic).
Based on the test results, it was concluded that an increase in the horizontal
reinforcement ratio had a small effect on the wall shear strength, but it was quite
beneficial with regards to the specimen deformation capacity.
Salonikios et al. (1999; 2000) reported on tests of low-rise shear walls detailed according
to the Eurocode 8 (EC8) provisions. Eleven specimens with a shear span-to-length ratio
of either 1.0 or 1.5 were tested under cyclic loading. The walls were reinforced for shear
with an orthogonal grid of web reinforcement, while some specimens had cross-inclined
bars also. Moderate levels of shear stress were recorded during the tests (
to (psi)) with the more slender walls sustaining an average drift of 1.5%
compared with 1.0% in the specimens with a shear span-to-length ratio of 1.0. Even
though web shear cracking was the first to be observed, all the specimens failed in a
15
predominantly flexural mode, characterized by concrete crushing and reinforcement
buckling at the confined wall edges. Diagonal cracking of the web and sliding at the wall
base were also observed, and the authors suggested that the degree of pinching was
controlled by bond-slip and horizontal sliding, rather than by the opening of inclined
shear cracks. The test results indicated that sliding shear resistance provided by the
diagonal bars led to an increase in the energy dissipation capacity of the walls with a
shear span-to-length ratio equal to 1.0. However, the effect of the diagonal reinforcement
was less significant for the walls with higher shear span-to-length ratios, particularly
when axial compression was present. Furthermore, no improvement in wall drift capacity
was observed with the addition of diagonal reinforcement. The authors also suggested
that walls with an aspect ratio of 1.5 and with low longitudinal reinforcement ratio in the
boundary region (boundary region reinforcing ratio as defined in the ACI Code less than
2.0%) could exhibit a flexural dominated behavior and as a result, the confinement of the
boundary region, rather than the shear reinforcement, is the critical design parameter.
Sittipunt et al. (2001) also evaluated the influence of diagonal reinforcement on the
hysteretic response of low-rise walls. In total, four barbell shape wall specimens with a
shear span-to-length ratio of 1.4 were tested to failure. Two walls contained conventional
web vertical and horizontal reinforcement, while the other two specimens were only
reinforced with a grid of inclined web reinforcement, as shown in Fig. 2-6. Web crushing
was reported in the walls reinforced with the conventional layout of web reinforcement,
whereas the diagonal reinforcement changed the failure mode in the other two specimens
to crushing of the concrete in the boundary elements. It should be noted that the wall
reinforcing details were appropriate for low to moderate seismicity regions and as a
result, the transverse reinforcement in the boundary elements was not intended to provide
confinement to the concrete core. The behavior of the walls with diagonal reinforcement
was quite similar to that reported by Salonikios et al. (1999; 2000), and was characterized
by a decrease in the shear distortions at the plastic hinge region compared with the
specimens with conventional web reinforcement. However, after yielding of the diagonal
reinforcement, the magnitude of shear distortions was comparable in all the specimens
with no appreciable effect on deformation capacity. Low-rise walls (shear span-to-length
16
ratio of 0.75) with diagonal reinforcement were also tested by Choi (2006) under a peak
shear stress ranging from to (psi). Similar conclusions to the study by
Sittipunt et al. (2001) were drawn from this study. The beneficial effect of the diagonal
reinforcement was also verified by an analytical study reported by Sittipunt and Wood
(1995) that showed that diagonal reinforcement provides a mechanism that is more
effective in transferring the lateral forces into the foundation, leads to lower shear strains
close to the base of the wall, and improves energy dissipation capacity. However, before
choosing the use of diagonal reinforcement in the web of walls, the difficulties associated
with the placement of the diagonal bars during construction should be considered.
Hidalgo et al. (2002) tested 26 low-rise walls with varying shear span-to-length ratios
(ranging from 0.35 to 1.0) under displacement reversals. The walls were designed to
exhibit a shear mode of failure in order to investigate the behavior of buildings with walls
exhibiting a non-ductile failure mode. The test set-up used in this investigation is shown
in Fig. 2-7. The research study indicated that deformation capacity of walls decreases as
the shear span-to-length ratio decreases, as reported by other investigators. Diagonal
cracking was observed at 0.1% drift, while drifts at failure varied from as low as 0.3% to
1.3%. No significant influence of the amount of distributed reinforcement on drift at first
cracking was observed, as expected. On the other hand, the amount of distributed web
reinforcement was found to somewhat affect the drift at ultimate. In contrast with
observations in other experimental projects, it was reported that the distributed web
reinforcement had little or no effect on the maximum shear strength. As noted by the
authors, however, the test setup had a significant influence on these observations since
these walls were tested under double curvature. It was also suggested that the energy
absorption capacity of the specimens was not influenced by the variation of wall aspect
ratio.
Lopes (2001(a); 2001(b)) reported on the tests of four walls with a shear span-to-length
ratio of 1.1. The test set-up is shown in Fig. 2-8 and the main parameters studied were the
amount and detailing of the horizontal and confinement reinforcement. The specimens
17
were tested under high shear stresses ( to (psi)) and exhibited the same
drift capacity (approximately 1.0%). No sliding shear failure was reported. Three
specimens failed in diagonal tension whereas one specimen (the wall that sustained the
higher shear stress) failed by concrete crushing. It was observed that the specimens that
failed in shear by diagonal tension achieved their ultimate loads at much lower levels of
displacement and had spalling of concrete at earlier stages compared with the specimen
that failed by concrete crushing. However, the specimens that failed in diagonal tension
exhibited a considerable ability to deform in the post-ultimate range with a moderate drop
in strength.
The issue of strength degradation with repeated loading cycles for low-rise walls has not
been widely investigated (Gulec et al., 2008). However, test results indicate that walls
subjected to load reversals often experience a significant loss of shear strength with
repeated cycling for displacements equal to or greater than the displacement
corresponding to the peak strength, as expected for all shear-critical elements. Also, a low
shear span aspect ratio is expected to have a significantly negative effect on the loss of
wall strength and stiffness (Salonikios et al., 1999; Hidalgo et al., 2002; Gulec et al.,
2008; 2009).
A summary of tests results from the experimental studies discussed above is presented in
Tables 2-1 and 2-2 for specimens with rectangular and barbell (or flanged) section,
respectively. It should be mentioned that in the reported tests various types of failure
modes were observed. Two important experimental results are presented: 1) the peak
shear stress; and 2) the lateral drift at ultimate. The peak shear stress, , was
calculated by dividing the maximum reported lateral load, , by the area bounded by
the wall thickness, , and the wall length, , i.e.:
(2-1)
18
The peak shear stress is expressed in multiples of (psi) to facilitate comparison
between the different tests and with available strength equations. The reported concrete
cylinder compressive strength was used as the value for . In cases where the authors
reported the cube compressive strength, the cylinder strength was estimated as 80% of the
cube strength (Mindess et al., 2003). Drift is defined as the ratio between the lateral
displacement at the point of the application of the load and the distance from this point to
the base of the wall. A sudden loss of strength or the point at which the load carrying
capacity dropped below 80% of the peak strength is taken as the ultimate condition in
these tables.
Besides the studies discussed above, several other results from monotonic and cyclic tests
on low-rise reinforced concrete structural walls are reported in the literature, but the test
set-up, scope of the investigation, test parameters, etc. were not relevant to the low-rise
walls tested for this study. For example, Palermo and Vecchio (2000) evaluated the
behavior of 3-dimensional flanged low-rise walls and concluded on the beneficial effect
of a minimal axial load, 5.4% of , on wall drift capacity. Gupta and Rangan (1998)
investigated the experimental behavior of barbell shape walls with a shear aspect ratio of
1.1 constructed with high-strength concrete ( in the range of 9 ksi to 14 ksi). Shake-
table tests of low-rise walls have also been reported by Mo and Kuo (1998). Wood
(1990), and more recently Gulec et al. (2008; 2009), compiled all the available test results
on isolated cantilever low-rise shear walls subjected to lateral load (monotonic or cyclic)
in order to study their shear strength. For an extensive list of experimental studies on low-
rise shear walls, the reader is referred to these two publications.
2.2.3 Design Philosophy and Review of Seismic Design Provisions for Reinforced
Concrete Walls in the 2005 ACI Code
Design criteria for reinforced concrete shear walls were first incorporated in the ACI
Committee 318 Building Code in 1971 (ACI Committee 381, 1971). As noted by
Cardenas et al. (1973), prior to publication of the 1971 ACI Code the only provisions for
19
the design of structural walls in the United States were those contained in the 1967 and
1970 Uniform Building Code (UBC 1967; 1970). Limited studies were available at that
time and most of the provisions in the early versions of the ACI Code were based on
experimental investigations undertaken by the Portland Cement Association (PCA) in the
late 1960s, and the subsequent recommendations by Cardenas et al. (1973). These early
provisions were basically intended to ensure that the walls possessed adequate shear
strength and the emphasis was on the evaluation of flexural and shear strength under
monotonic loading.
The 2005 ACI Code design requirements for structural walls located in regions of high
seismicity are given in Section 21.9, “Special structural walls and coupling beams” (ACI
Committee 318, 2005). The reinforcement in structural walls typically included
distributed vertical and horizontal reinforcement spread uniformly over the length and the
height of the wall, respectively. Well distributed reinforcement is generally preferred in
the walls because it provides cracking control to the diagonal compression strut and
improves the conditions for dowel action, which in turn enhances the sliding shear
resistance at the base of the wall (Pauley et al., 1982). Concentrated vertical
reinforcement is usually placed at the edges of the wall (referred to as the “boundary
elements”) and is tied with transverse reinforcement. Minimum reinforcing ratios and
maximum allowable spacing for the web distributed reinforcement follows the ACI Code
provisions for ordinary shear walls (Section 11.9.9 of 2005 ACI Code). The required
minimum ratio of horizontal reinforcement area to gross area of the wall is specified as
0.0025. In addition, for low-rise walls (wall height-to-length ratio, ),
it is required that the vertical reinforcing ratio be no less than the horizontal reinforcing
ratio, recognizing the observation reported by several researchers that the vertical
reinforcement in low-rise walls is more efficient than the horizontal reinforcement in
controlling the width and growth of diagonal cracks (Cardenas, 1973; Barda et al., 1977;
Wood, 1990; Lefas et al., 1990).
20
During strong seismic excitations, structural walls will likely undergo inelastic
deformations, since it is not practical to design a structural wall to remain elastic during
such events (Wallace and Moehle, 1992). But when inelastic deformations are allowed,
usually occurring at the wall base, the wall must be specially detailed at those critical
regions. Special transverse reinforcement should be provided at the wall edges, when
high compression demands (stress and/or strain) are expected, to avoid early concrete
crushing and to prevent or delay buckling of the longitudinal reinforcement so that
adequate ductility can be achieved. The evaluation for need of “special boundary
elements” can be carried out either through a stress-based check or a displacement-based
approach.
Prior to 1994, strength requirements were primarily governing the design of reinforced
concrete structural walls in the U.S. code provisions, for example, the 1989 ACI Code
(ACI Committee 318, 1989) and the 1991 UBC Code (UBC, 1991). As a result, the
stress-based approach for evaluating the need for special boundary elements was used in
the 1989 ACI Code and the 1991 UBC Code (Thomsen and Wallace, 2004). The required
deformability was achieved through the use of heavily confined boundary elements when
the extreme fiber stress due to combined axial and lateral loads exceeded psi. This
evaluation was performed using a linear elastic analysis with element stiffness values
based on gross concrete cross-sectional dimensions. It was also required to continue the
special transverse reinforcement at the wall boundaries up to the wall height at which the
computed stress was less than (Wallace and Orakcal, 2002; Thomsen and
Wallace, 2004).
A displacement-based design methodology for shear walls was proposed in the early
1990s (Moehle and Wallace, 1989; 1994, Wallace and Moehle, 1992) and presented an
alternative and less conservative design for the boundary regions of shear walls compared
with the “stress-based” approach. Based on these studies, new provisions for evaluating
the need for special detailing requirements using a “displacement-based” approach were
first incorporated in the 1994 UBC Code and later in the 1999 ACI Code (ACI
21
Committee 318, 1999). Using the displacement-based approach, the need for boundary
elements is evaluated based on the maximum strain demand calculated from an estimated
plastic hinge rotation (or drift) demand. Section 21.9.6.2 of the 2005 ACI Code (ACI
Committee 318, 2005) requires that structural walls be detailed with special boundary
elements when:
(2-2)
where c is the neutral axis depth, is the design lateral displacement and should
not be less than 0.007. The 2005 ACI Code also states that the “boundary elements
should extend horizontally from the extreme compression fiber a distance not less than
the larger of and ”. For flanged wall sections, it is also required that the
boundary element be extended at least 12 in. into the web.
Eq. (2-2) was developed assuming that special detailing should be provided when the
compression strain at the extreme fiber exceeds a limiting value of 0.004 (Wallace and
Orakcal, 2002). The wall height over which confinement should extend, specified as the
larger of and , (where and refer to the factored moment and shear
force at the critical wall section, respectively) is based on a conservative estimate of the
plastic hinge length for structural walls (Paulay, 1986; Wallace, 1994). The stress-based
approach is still maintained in the 2005 ACI Code (ACI Committee 318, 2005), mainly to
address configurations where the displacement approach is not appropriate (for example
perforated walls or walls with setbacks) (Wallace and Orakcal, 2002). It can also be
argued that the check for boundary elements in walls highly dominated by shear, such as
walls with very low shear span-to-length ratios, should be based on the stress check,
because in such cases the assumption of plane sections remaining plane after loading is
not valid (Wallace, 1995(b)). In slender walls, particular attention to the confinement
reinforcement is required for asymmetrical walls or walls with high levels of axial stress,
but generally the “displacement-based” approach is less stringent for evaluating the need
22
for special transverse reinforcement when compared to the “stress-based” approach
(Wallace and Moehle, 1989; Wallace, 1995(a)
).
When special boundary elements are required in structural walls, the confining
reinforcement should not be less than (Section 21.9.6.4 of the 2005 ACI Code):
(2-3)
where is the total cross-sectional area of the confinement reinforcement
perpendicular to , is the transverse spacing of the confinement reinforcement, is
the concrete core dimension perpendicular to the tie legs that constitute , and is
the specified yield strength of the confinement reinforcement. In addition, the spacing, ,
should not exceed: (a) one-quarter of the minimum member dimension, (b) six times the
diameter of the smallest longitudinal bar, and (c) the quantity , defined as follows:
(2-4)
where, is taken as the largest centerline to centerline distance between tie legs used in
the boundary elements.
The requirements for the flexural and axial load strength of walls are contained in Section
21.6.5.1 of the 2005 ACI Code (ACI Committee 318, 2005). A strain-compatibility
analysis assuming plane sections (linear strain distribution) is allowed to be used to
assess flexural strength. Before the 1999 edition of the ACI Code, the web vertical
reinforcement contribution to the wall flexural strength was neglected and the boundary
elements were required to resist the full overturning moment and axial load. The
application of this requirement resulted in flexural overstrength of the wall, with
important implications on wall shear demand and the forces in the foundations. However,
based on the 2005 edition of the ACI Code, reinforcement in the boundary elements and
the web of the wall should be included in the strength calculations.
23
It should be noted that the provisions of the 2005 ACI Code for “Special structural walls”
are basically the same as in the latest edition of the code published in 2008 ((ACI
Committee 318, 2008). The only change in the 2008 edition of the code was with respect
to the 2005 provision that the spacing of the confinement reinforcement in the boundary
elements should not exceed one-quarter of the minimum member dimension. In the 2008
ACI Code, one-third of the minimum member dimension is allowed as maximum
spacing.
2.2.4 Estimation of Shear Strength of Low-Rise Reinforced Concrete Structural
Walls
Equations for the estimation of maximum shear strength of reinforced concrete shear
walls can be found in building codes and the literature in general. A number of
parameters have been found to affect the wall strength, such as wall aspect ratio, vertical
and horizontal web reinforcement ratio, concrete strength, and applied axial force (Gulec
et al., 2008; 2009). Some of these expressions are discussed next. The reader should be
aware, however, of the significant scatter observed when comparing predicted resuls for
the shear strength (Wood, 1990, Gulec et al 2008; 2009).
2.2.4.1 2005 ACI Code and Eurocode EC8
The 2005 ACI Code (ACI Committee 318, 2005), which is widely used in earthquake-
prone regions, provides two sets of equations to determine the nominal shear strength of
walls. The same equations are given in the 2008 edition of the ACI Code. One equation is
given in Section 21.7 (Special reinforced concrete structural walls and coupling beams)
and is indented to be used for seismic design. The second equation is used for general
design and is given in Section 11.10 (Special provisions for walls). Both equations are
semi-empirical and are based on the widely used modified truss analogy (Cardenas, 1973;
Wood, 1990). Based on the modified truss analogy, the nominal shear strength of
structural walls is attributed to the contribution of the steel reinforcement and
the contribution of the “concrete” . The concrete contribution consists of the shear
24
carried in the compression zone, dowel action and aggregate interlock, whereas steel
contribution refers to shear carried by horizontal web reinforcement through a truss
action.
The nominal shear strength expression for concrete walls in Section 21.7 of the 2005 ACI
Code (also the same in 2008 ACI Code) has the following form, in U.S. customary units:
(2-5)
where is an aspect ratio coefficient that varies linearly from 3.0 (psi units) for walls
with wall height-to-length ratio, , less than 1.5, to 2.0 for walls with a ratio greater
than 2.0, is the compressive strength of the concrete (psi units), is the horizontal
web reinforcement ratio, is the yield strength of the horizontal reinforcement (psi
units), and is the area of the wall bounded by the wall thickness and the wall length
(in2
units). Eq. (2-5) clearly recognizes the higher shear strength in walls with low height-
to-length ratio by specifying a concrete contribution of (psi) for height-to-length
ratios less that 1.5, reducing it to (psi) for ratios greater than 2.0. This provision
accounts indirectly for the beneficial effect of resisting part of the shear through a direct
diagonal compression strut for short walls (Salonikios et al., 1999). Also, recognizing that
web crushing is a potential limit on the capacity of structural walls, an upper limit of
(psi) is imposed on the wall shear stress. This limit is based mainly
recommendations by Cardenas et al. (1973), but tests by Oesterle et al. (1984) indicated
that this limit may not eliminate web crushing as a possible failure mode for walls
subjected to extremely large inelastic deformations, especially for walls with concrete
compressive strength lower than 5000 psi and subjected to low axial stresses.
The nominal shear strength equations for walls constructed with normal weight concrete,
as given in Section 11.10 of the 2008 ACI Code (non-seismic design), is described below
in U.S. customary units:
25
(2-6)
(2-7)
(2-8)
(2-9)
where is the wall thickness (in.), is the effective depth which can be assumed equal
to (in.), is the axial load which is negative in tension (lbs), is the factored
moment at the section under consideration (lbs-in.), is the area of the horizontal
reinforcement within a distance s (in.2
) and s is the spacing of the wall horizontal
reinforcement (in.). The contribution of the concrete is taken as the lesser of the values
provided by Eqs. (2-7) and (2-8). The first equation for the concrete contribution (Eq. 2-
7) was derived for web-shear cracking and mostly applies to low-rise shear walls
(Cardenas et al., 1973), whereas the second equation (Eq. 2-8) corresponds to flexural-
shear cracking. It should be also mentioned that Eq. (2-8) does not apply when:
(2-10)
The provisions in the current Eurocode EC8 (CEN Technical Committee 250/SC8) for
the estimation of the shear strength of shear walls are more complicated compared with
those in Section 21.7 of ACI Code. Eurocode 8 provides separate equations for the shear
resistance of structural walls subjected to seismic loading, based on the different possible
failure modes, namely diagonal tension, diagonal compression (including web crushing),
and sliding shear. Similarly to the ACI Code provisions, the equation for diagonal tension
resistance is based on the modified truss analogy. But in contrast to the ACI provisions,
Eurocode 8 provisions do not account for any increase in concrete contribution in walls
26
with low aspect ratio. In addition, the contribution to shear strength from web
reinforcement in Eurocode 8 is estimated on the basis of the moment-to-shear ratio
. The design equation recommended in Eurocode 8 implies that for
, only horizontal reinforcement contributes to shear strength, whereas for
, only the vertical reinforcement resists shear; both types of reinforcement are
considered effective for intermediate values.
Another important difference between American and European practice concerns the
possibility of sliding shear failure of low-rise walls, which is recognized in the Eurocode
8 and a corresponding design procedure is suggested. The resistance of walls against
sliding shear, according to Eurocode 8, is assumed to be made up of contributions from
dowel action of vertical bars, shear resistance of cross-inclined bars, and frictional
resistance. The possibility of sliding shear failure is not explicitly accounted for in the
ACI Code. However, it is believed to be indirectly addressed by the upper limit to the
nominal shear stress of (psi) (Salonikios et al., 1999). It is worth pointing out that
the equations concerning wall shear resistance against sliding shear currently specified in
the Eurocode 8 provisions are quite complex and mostly semi-empirical, and were
developed using the recommendations by Pauley et al. (1982).
2.2.4.2 Wood (1990)
Wood (1990) made an extensive investigation in order to collect, compile and evaluate
test data of low-rise concrete walls subjected to lateral loads. The investigation focused
on laboratory tests of one- and two-story isolated reinforced concrete walls (rectangular,
barbell or flanged) with shear span-to-length ratios less than 2.0. The selected specimens
were tested under either lateral monotonic loading or lateral load reversals. The compiled
data showed a significant scatter with regards to the reported maximum average shear
stress for low-rise walls, but a trend of increasing maximum average shear stress with an
increase in the product (where is the horizontal web reinforcement ratio) was
27
verified. Specimen size did not seem to affect shear strength for the sizes considered
while the loading scheme was found to have a negligible influence. Wood (1990) pointed
out that the modified truss analogy appeared to overestimate the rate of increase of shear
strength attributable to the web reinforcement in low-rise walls and as a result, the 1983
ACI Code (ACI Committee 318, 1983) equations for shear tended to underestimate the
nominal shear strength of lightly reinforced walls and to overestimate the strength walls
with more than 1.5 times the minimum web reinforcement ratio of 0.25%. A lower bound
of (psi) was recommended for the shear strength of low-rise walls with minimum
distributed web reinforcement ratios, which seemed independent of web reinforcement
ratio. In the same study, it was proposed that an increase in the shear strength beyond this
lower bound could be attributed to the contribution of the vertical reinforcement
(longitudinal reinforcement in the boundary elements and web vertical reinforcement),
which can be approximated using a friction model. The shear stress upper limit of
(psi) in the ACI Code, and also suggested by several researchers (for example Cardenas
et al., 1973), was considered to be reasonable. In summary, the work by Wood (1990)
resulted in the following equation for predicting the shear strength of low-rise walls in
U.S. customary units:
(2-11)
where is the area of total vertical reinforcement (sum of web and boundary element
reinforcement) crossing the shear plane (in.2
) and is the reinforcement yield stress for
the combination of vertical web and boundary element reinforcement (psi units).
2.2.4.3 Barda et al. (1977)
Barda et al. (1977) proposed an equation for the prediction of the shear strength of low-
rise walls, based on test results and the use of the truss analogy. An alternate formulation
for the “concrete” contribution to shear strength was recommended because the ACI
Code provisions that were in effect at the time (ACI Committee 318, 1971) were found to
be quite conservative. The proposed equation is as follows, in U.S. customary units:
28
(2-12)
where is the vertical web reinforcement ratio, is the yield stress of the vertical web
reinforcement (psi units), and is the distance from the extreme compression fiber to
centroid of wall vertical reinforcement in tension (in.). No upper limit for the shear
strength was proposed in the study.
2.2.4.4 Comments on the Design Equations for Shear Strength of RC Low-Rise Walls
Recently, Gulec et al. (2008; 2009) compiled most of the existing tests results for low-
rise walls with rectangular cross section as well as with boundary barbells or flanges and
reported on the adequacy of several equations for predicting wall shear strength. The
investigation led to the conclusion that the equation proposed by Wood (1990) gave the
best prediction of the peak shear strength of rectangular low-rise walls and in most cases,
the proposed lower limit of (psi) governed the shear strength. The procedure of
Barda et al. (1977) discussed above was found to overestimate the peak shear strength of
rectangular walls and the authors recommended that it should not be used in walls with
rectangular cross section. On the other hand, in walls with boundary elements (barbells or
flanges), even though Wood’s equation gave generally quite conservative results, the
equation of Barda et al. led to reasonable estimates of the peak shear strength, especially
for heavily reinforced walls. Gulec et al. (2009) also commented on the significant scatter
of the peak shear strength predicted using different equations and on the lack of
procedures that consider the influence of the barbell or flange area on the shear
resistance, as well as the effect of out-of-plane loading.
With regards to the Eurocode 8 provisions, based on the experimental investigation
conducted by Salonikios et al. (1999; 2000), it was demonstrated that the calculated
sliding shear capacity of low-rise walls, based on the equations in Eurocode 8,
significantly underestimated the measured maximum shear. Salonikios et al. (2000) also
concluded that the Eurocode 8 estimation for shear resistance corresponding to diagonal
29
tension failure tends to be more conservative than the equation in the 1999 ACI Code
(ACI Committee 318, 1999), which is the same equation as in the 2005 and 2008 ACI
Code.
2.3 BEHAVIOR AND STRUCTURAL APPLICATIONS OF HIGH
PERFORMANCE FIBER REINFORCED CONCRETE (HPFRC)
2.3.1 Overview and General Characteristics of HPFRC
Fiber reinforced cementitious composites (FRCCs) consist of concrete or mortar
reinforced with discontinuous fibers, which provide post-cracking tensile resistance. The
beneficial effects of the addition of discontinuous fibers to the concrete or mortar have
been realized by engineers since the turn of the last century, but this technology was not
extensively developed until the early 1960s (Naaman, 1985). Several fiber materials and
cross sectional shapes have been used with different results, including steel (flat,
crimped, hooked, twisted), polypropylene (PP), polyvinyl alcohol (PVA), glass, and
carbon fibers. Since the 1990s, production of higher strength fiber reinforced concrete,
use of polymers that enhance the fiber-mortar interaction, and development of polymer-
based and high strength steel fibers, are just some of the technological improvements in
the field of fiber reinforced concrete.
High-Performance Fiber Reinforced Cementitious Composites (HPFRCCs) and High-
Performance Fiber Reinforced Concrete (HPFRC) are a special category of Fiber
Reinforced Cementitious Composites (FRCCs) and are defined as those that develop a
pseudo strain-hardening behavior in tension (Naaman and Reinhardt, 1996). In this
report, the term HPFRC will be used to describe both materials for simplicity. However,
a distinction will be made in cases where no coarse aggregate (i.e. mortar mixture) was
used in the HPFRC mixture.
Nowadays, a pseudo strain-hardening behavior in tension can be achieved with the use of
relatively low volume fraction of fibers, typically lower than 2.0% (Parra, 2005).
30
Multiple cracking and high energy absorption capacity are typically observed with this
pseudo strain-hardening behavior. A qualitative stress-strain behavior of an HPFRC
material is illustrated in Fig. 2-9 (Naaman, 1998). It should be mentioned that not all fiber
types can lead to this high-performance behavior, and the fiber content required to
achieve strain-hardening behavior highly depends on the fibers, matrix properties and
fiber-matrix interaction. Steel fibers (hooked and twisted) and ultra-high molecular-
weight polyethylene (Spectra) fibers have been used to develop HPFRC materials with
successful applications in earthquake-resistant structures (Parra, 2005). Factors that have
been reported to affect the tensile and compression response of FRCC and HPFRC
materials include fiber volume fraction, fiber material and geometry, cementitious matrix
composition, average bond strength versus slip response along the fiber-matrix interface,
and distribution of fibers in the mix (Naaman, 1998).
The compressive stress-strain properties of FRCC and HPFRC materials with various
types of fibers have been extensively studied (for example Shah and Rangan, 1971; Shah
and Naaman, 1976; Shah et al., 1978). In those investigations, it was found that the
compressive strength of the mortar or concrete is not appreciably improved by the
addition of fibers, unless a high volume of fibers is used. However, a significant
enhancement in compression ductility is possible, especially in the case of HPFRC,
which can sustain large compression strains with no material spalling because the fibers
can resist the lateral expansion and preserve the concrete integrity. In tension, the
response of HPFRC is characterized by a nearly linear behavior up to first cracking,
followed by a pseudo-strain hardening region up to the strain at which crack saturation
damage localization) occurs, typically observed at strains in the range of 2.0% to 5.0%
(Naaman and Reinhardt, 1996). Overall, the superior ductile tensile performance of
HPFRC materials leads to a multiple cracking pattern, with smaller crack widths and
generally superior damage tolerance in structural elements.
31
2.3.2 Shear Strength of Fiber Reinforced Cementitious Composite (FRCC)
Members
It can be argued that the parameters that influence the shear resistance of FRCC members
include those that affect the shear strength of conventional reinforced concrete members,
with the additional significant contribution from the post-cracking tensile strength of the
FRCC material (Khuntia et al., 1999). However, little is known about the interaction
between the shear resistance provided by the fibers and that provided by the concrete and
the steel reinforcement (Chompreda and Parra, 2005). As a result, the development of
expressions that predict the ultimate shear strength of FRCC members, either through
analytical work or experimental investigations, is quite challenging. Most of the studies
available refer to the shear behavior of FRCC beams and provide semi-empirical strength
equations that are mainly applicable to slender beams under monotonic loading (for
example Ashour et al., 1992; Li et al., 1992; Mansur et al., 1986; Narayanan and
Darwish, 1987; Sharma, 1986). Little is therefore known about the shear strength FRCC
and HPFRC members subjected to displacement reversals.
A common approach in many predictive equations for the shear strength of FRCC beams
is based on the idea of the modified “truss model” that is used in conventional reinforced
concrete members for shear strength predictions, but including an additional independent
term for the contribution of the fibers, . As a result, an equation of this general form is
as follows:
(2-13)
The contribution on the fibers in many equations is dependant, among others, on the fiber
volume fraction and aspect ratio, the beam aspect ratio, and the anchorage conditions for
the fibers (Kwak et al., 2002). Narayanan and Darwish (1988) reported that the beneficial
effect of arch action that is present in deep members, and usually reflected in the “ ”
term, improves noticeably with the inclusion of steel fibers, which control the growth of
splitting cracks.
32
Narayanan and Darwish (1987), based on tests of FRCC beams with no stirrups,
proposed the following equation for the contribution of the fibers and the concrete, in
MPa:
(2-14)
where is the shear span length (mm), is the beam effective depth (mm), is the split
cylinder strength of the FRCC (MPa), is tensile reinforcement ratio, is the fiber-
matrix interfacial bond stress, and is a fiber factor defined as:
(2-15)
where is a bond factor that accounts for the shape and surface characteristic of the
fiber, is the fiber volume fraction (%), is the fiber length (mm), and is the
diameter of the fiber (mm). In this equation, the contribution of the “concrete”, , is
assumed dependant on the split-cylinder strength of the FRCC, while one of the most
significant parameters in evaluating the fiber contribution is the fiber-matrix interface
bond. It should be noted, however, that this quantity is very difficult to estimate (Khuntia
et al., 1999), which poses severe limitations on the applicability of this type of design
equation.
Khuntia et al. (1999) proposed a simple equation for the shear strength of FRCC
members without transverse reinforcement subjected to monotonic loading, which can be
applied to both slender and deep beams, in MPa:
(2-16)
where is the cylinder compressive strength of FRCC (MPa) and is defined as:
33
(2-17)
It should be mentioned that Eq. (2-16) was developed by collecting data from several
research projects that focused on the use of straight, crimped, and hooked steel fibers.
The equation is quite conservative and assumes correlation between the post-cracking
strength, , and compressive strength ( ), which may not be adequate for
some types of fibers. In addition, it assumes (MPa).
The above mentioned equations assume a somewhat independent contribution of the
concrete and the fibers. A different approach could be based on the Modified
Compression Field Theory (Vecchio and Collins, 1986), which relates the “ ” term in
reinforced concrete beams to the tensile stress carried by the concrete in between the
cracks. It could be argued, therefore, that the contributions from the concrete and the
fibers are related and may be lumped into a single term. However, this possibility
requires further investigation.
2.3.3 Application of HPFRC in Shear-Critical Elements Subjected to Displacement
Reversals
The ductile behavior of HPRFC, characterized by multiple cracking, high energy
absorption, and superior deformation capacity, has led researchers to explore the
application of HPFRC in earthquake-resistant structures. In such structures, the behavior
is mainly controlled by the regions where the inelastic activity occurs and therefore, the
use of HPFRC in those critical regions is very attractive because the superior deformation
capacity and damage tolerance of HPFRC can significantly enhance structural behavior,
while allowing for simplifications in reinforcement detailing. Experimental studies have
verified that the addition of fibers to the cementitious matrix has favorable effects in
terms of shear strength, shear deformation capacity, and stiffness retention, especially for
34
shear-critical reinforced concrete elements subjected to cyclic loading when compared
with the response of traditionally reinforced concrete members (Parra, 2003).
Applications of HPFRC in shear-critical elements include column-beam connections,
plastic hinges in flexural members under high shear, structural walls, coupling beams,
precast concrete frame conections, and precast infill panels for seismic retrofit of
buildings. Most of the investigations on the application of HPFRC in earthquake-resistant
structures have been conducted at the University of Michigan and a brief discussion of
some of these experimental investigations is reviewed in the following paragraphs.
The use of FRCCs with hooked-end steel fibers in reinforced concrete coupling beams
was investigated by Wight and Erki (1995). The experimental results indicated that the
use of an FRCC material with 1.5% volume fraction of hooked steel fibers in diagonally
reinforced coupling beams, where the confinement around the diagonal bars was
eliminated, exhibited a superior performance to diagonally reinforced coupling beams
with standard detailing. Canbolat et al. (2005) further investigated the behavior of
HPFRC (mortar mixture) diagonally reinforced beams and verified that a simplification
in the reinforcement detailing is possible in coupling beams. Fig. 2-10 shows the
reinforcing detailing of the four coupling beam specimens of the study by Canbolat et al.
(2005). Specimen 1 was designed according to the seismic provisions of the ACI Code
and constructed with regular concrete, whereas the other three specimens were
constructed with an HPFRC material. In this study, it was found that the use of HPFRC
may result in the elimination of transverse reinforcement around diagonal bars since the
HPFRC material can provide adequate confinement to prevent the buckling of those bars.
Specimens with either 2% volume fraction of ultra-high molecular weight polyethylene
(Spectra) fibers or 1.5% volume fraction of steel Torex (twisted) fibers exhibited
enhanced performance compared to that of well detailed coupling beams. Both HPFRC
coupling beams exhibited substantially higher shear strength and energy dissipation
capacity with a superior damage tolerance, characterized by less concrete spalling and a
dense network of microcracks up to damage localization. Even after a fiber pullout had
occurred due to diagonal tension, the HPFRC material was able to provide confinement
to the diagonal bars.
35
An attractive application for FRCCs and HPFRC is in connections between beams and
columns in reinforced concrete frame structures, where the required reinforcement
detailing leads to significant reinforcement congestion in the joint region. Henager (1977)
investigated the behavior of a beam-column connection, constructed with an FRC with a
1.7% volume fraction of steel fibers, where all the column stirrups in the joint region
were eliminated. An increase in strength, stiffness and damage tolerance was reported for
the FRCC joint, compared with the behavior of a control specimen detailed according to
the 1971 ACI Code (ACI Committee 318, 1971). The results were further verified by
later experimental studies conducted by Craig et al. (1984) and Filiatrault et al. (1994;
1995). Parra and Wight (2000) also demonstrated the possibility for reduction and even
elimination of the transverse reinforcement in RC Column-to-Steel Beam (RCS)
connections while increasing bearing strength with the use of an HPFRC material
(Engineered Cementitious Composite – ECC [Li, 1993]) with a 1.5% volume fraction of
ultrahigh molecular weight polyethylene (Spectra) fibers. A peak shear distortion of
about 2.0% was reported for the HPFRC connection, with only minor damage, as well as
an enhancement in strength in comparison with a standard RCS connection tested for
comparison purposes.
Besides the use of HPFRC material in shear-dominated members, Parra and Chompreda
(2007) investigated the use of HPFRC (mortar mixture) in the plastic hinge region of
beams subjected to shear reversals. The goal was to study the shear strength decay and a
potential reduction in transverse reinforcement requirements in HPFRC flexural members
under inelastic displacement reversals. The beam specimens were constructed with an
HPFRC (mortar) that contained either Spectra or hooked steel fibers in volume fractions
of 1.5% and 2.0%, respectively. The results showed a very promising application for
HPFRC, since all the specimens exhibited a stable hysteretic response at drifts exceeding
4.0%. At this drift level, only hairline crack formation was visible in the beam plastic
hinge region, except for the beam-column interface, and no buckling of the longitudinal
bars was observed, indication that the HPFRC can provide significant confinement to the
bars, even when no transverse reinforcement was used. An important general conclusion
36
from the study was that a shear strength of (psi) represented a lower limit for the
shear resistance of HPFRC members, regardless of the rotation demand.
2.3.4 Application of FRCC Materials in Structural Walls Kim and Parra (2003) investigated the hysteretic response of low-rise walls constructed
with an HPFRC material (mortar mixture) containing either steel or Spectra fibers in a
2.0% and 1.5% volume fraction, respectively. Two low-rise walls with a shear span to-
wall length ratio of 1.5 were tested under reversed cyclic displacements. Web vertical and
horizontal distributed reinforcing ratios were less than the minimum reinforcing ratio of
0.25% specified in the ACI Code and equal to 0.21% and 0.13%, respectively. In
addition, no special transverse reinforcement was used in the wall boundary regions. The
wall specimens exhibited only moderate damage at 1.5% drift and a drift capacity of
approximately 2.0%. Hysteresis loops were stable up to a maximum shear deformation of
approximately 2.0%. Multiple cracking was observed with crack widths less than 2 mm
up to 1.5% drift. Further, no instability was observed in the wall edges, despite the lack of
special confining reinforcement and the high compressive stresses developed. It was also
estimated that about 80% of the wall diagonal tension capacity was attributed to the
fibers. The results of the tests performed by Kim and Parra (2003) showed the potential
for a new simplified design for low-rise structural walls that can lead to enhanced
displacement capacity and damage tolerance while allowing for a relaxation of wall web
and confinement reinforcement requirements. These tests served as a pilot study for the
investigation presented in this report. Further details with analysis of test results are
provided in Chapters 4 and 5.
A study of the behavior of slender structural walls constructed with FRCC material was
conducted by Parra et al. (2006). The main goal of the study was to eliminate the
confinement reinforcement in the special boundary regions of the walls through the use
of FRCC in the wall plastic hinge region. One wall was designed according to the seismic
provisions of the 2002 ACI Code (ACI Committee 318, 2002), whereas three specimens
were constructed with FRCC in the plastic hinge region. The FRCCs evaluated contained
37
steel fibers in either a 1.5% or 2.0% volume fraction. Even though special confinement
was not used in the boundary regions of the FRC walls, the drift capacity of the
specimens ranged from 2.5% to 3.0%. A wall specimen with 2.0% volume fraction of
hooked steel fibers (HPFRC mortar material) exhibited superior damage tolerance, no
instability of the boundary regions, and failed due to fracture of the main longitudinal
reinforcement at 3.5% drift. The test results indicated that all the FRC walls had a
flexure-dominated response, as opposed to the RC specimen, which exhibited significant
shear-related damage at the end of the test. This RC wall, designed according to Chapter
21 of the 2002 ACI Code, behaved well when subjected to cycles up to 3.5% drift,
despite the substantial shear related damage during the later loading cycles.
Buzzini et al. (2006) reported on three tests of structural walls constructed with Hybrid
Fiber Concrete (HFC). HFC refers to a high-strength HPFRC with self-compacting
properties that contains a mix of fibers of different shapes (straight, crimped and hooked)
and of various lengths that are added to a mortar in volume fractions ranging from 1% to
4% (Markovic et al., 2003; 2004). Buzzini et al. (2006) investigated the behavior of two
slender walls with a rectangular cross-section and a shear span-to-wall length ratio of 2.8.
An additional wall with a barbell shape and a shear span-to-wall length ratio of 1.9 was
also tested. All the walls had the same amount of flexural reinforcement and web vertical
reinforcement, but neither horizontal web reinforcement nor transverse reinforcement in
the boundary regions was provided, such as to evaluate the efficiency of the fibers to
provide shear resistance and confinement. A cold joint existed in all the specimens
between the wall and the foundation and sliding shear deformations significantly
influenced the hysteretic behavior of the specimens. The authors suggested placing
sleeves in the longitudinal bars close to the footing so as to prevent bond between the
longitudinal bars and the concrete and spread the yielding of the longitudinal bars over a
larger region. All the specimens showed a stable hysteretic behavior, with a drift capacity
ranging from 3.2% to 4.0%. Minimum concrete spalling was reported at failure, which
occurred due to fracture of the longitudinal reinforcement. Overall, a superior
serviceability and adequate inelastic deformation capacity was reported for all the
specimens when compared to conventional reinforced concrete structural walls. It should
38
be noted, however, that in these tests, the applied shear stress level was low and ranged
from to (psi).
2.4 SUMMARY
The design of reinforced concrete structural walls to sustain the deformation demands
imposed by strong ground motions requires the use of special reinforcement details to
ensure adequate inelastic displacement capacity. These reinforcement requirements
consist of a grid of vertical and horizontal web reinforcement and special confining
reinforcement in the wall boundary elements. Construction difficulties and reinforcement
congestion are usually associated with this detailing. Even though the desired level of
shear strength can be achieved with the current design philosophy, there is evidence that
low-rise walls posses limited displacement and energy dissipation capacity. Furthermore,
no comprehensive information is available on the relation between wall drift capacity and
shear stress demand. Researchers have proposed the use of diagonal reinforcement in the
web of the wall to enhance overall behavior, as well as resistance against sliding shear.
However, before choosing the use of inclined reinforcement on the web of walls, the
difficulties associated with the placement of the diagonal bars during construction should
be considered.
A potential simplified reinforcement detailing, consisting of relaxed requirements for the
wall distributed reinforcement and partial or even total elimination of the confinement
reinforcement in the boundary regions can potentially be achieved through the use of
randomly oriented fiber reinforcement. Results from prior research have shown that the
use of strain-hardening fiber reinforced cement composites in shear-critical elements
(coupling beams, beam-column connections, and shear walls) can enhance their
performance in terms of deformation capacity and damage tolerance. Experimental
research has also shown that fiber reinforcement can be used to partially replace
confinement and shear reinforcement, without any compromise in terms of strength and
ductility.
39
Prior to this research, very limited information was available on the behavior of low-rise
walls constructed with High-Performance Fiber Reinforced Concrete (HPFRC). Thus, a
comprehensive experimental research program was undertaken with the goal of
generating required information in order to understand the hysteretic behavior of HPFRC
low-rise walls and propose an alternative simplified design for these walls when used in
regions of high seismicity. The results of this study will also help to better understand the
seismic behavior of RC and HPFRC low-rise walls and the influence of several
parameters, most importantly wall aspect ratio and shear stress demand, on wall behavior.
40
CHAPTER 3
EXPERIMENTAL PROGRAM
3.1 INTRODUCTION
The purpose of this research program was to investigate the inelastic behavior of High-
Performance Fiber Reinforced Concrete (HPFRC) low-rise structural walls, with
emphasis on their displacement capacity, shear behavior and damage tolerance. As
described in Section 2.2.4, two HPFRC low-rise walls were tested under large
displacement reversals in a previous study conducted by Kim and Parra (2003). The
reported results showed great potential, through the use of HPRC materials, for a
significant reduction in the confining reinforcement in the wall boundary regions, as well
as a relaxation in distributed web reinforcement. In this investigation, seven low-rise
walls constructed with either HPFRC or conventional reinforced concrete were tested to
further evaluate the application of HPFRC materials in low-rise structural walls, which
could result in an simplified reinforcement detailing without compromising seismic
performance.
Based on past experimental investigations, discussed in Section 2.1.2, several parameters
have been found to affect the behavior of reinforced concrete low-rise walls, including
wall configuration, aspect ratio, amount and layout of web reinforcement, shear stress
level, and axial load. The series of tests conducted in this research project were designed
to study the influence of the following factors on the seismic response of reinforced
concrete and HPFRC low-rise walls:
41
• average shear stress level;
• wall aspect ratio;
• web reinforcement ratio;
• tension reinforcement ratio;
• use of fiber reinforced concrete versus fiber reinforced mortar; and
• use of dowel reinforcement at the base of the wall.
In the following sections, a detailed description of the tests conducted, including the
materials used, specimen geometry and design, and test set up and instrumentation, is
presented. Details of the specimens tested by Kim and Parra (2003) are also given
because the results from these tests are compared with those of a companion RC
specimen tested as part of this study.
3.2 TEST SPECIMENS
3.2.1 General Description of Test Specimens
Nine large-scale cantilever low-rise wall specimens were constructed and tested under
displacement reversals in the Structural Engineering Laboratory at the University of
Michigan. Seven of the specimens were tested by the writer, whereas two specimens
were part of a preliminary study on HPFRC low-rise walls conducted by Kim and Parra
(2003). The dimensions of the test specimens are shown in Fig. 3-1. Each specimen
consisted of a wall fixed connected to a 72 in. long, 24 in. deep and 24 in. wide heavily
reinforced concrete base block anchored to the laboratory strong floor. A 16 in. deep by
16 in. wide reinforced concrete top block was used for loading purposes. The load was
applied through a hydraulic actuator connected to the mid-depth of the top beam at one
end and to the laboratory reaction wall at the other end. The bottom and top blocks in all
the specimens were constructed with regular concrete, whereas the wall was constructed
with either regular concrete or an HPFRC mixture, depending on the design parameters
of the specimen.
42
In all the specimens, the wall had a rectangular cross section, 40 in. long and 4.0 in thick.
In order to investigate the influence of the wall height-to-length ratio on the
behavior of reinforced concrete and HPFRC low-rise walls, two different ratios were
considered for the wall specimens. In one group of specimens, the wall had a height of 40
in., which translated into a wall height-to-length ratio of 1.0. For the rest of the
specimens, the height-to-length ratio was 1.3, leading to a wall height of 52 in. The ratio
between the shear span, , i.e. the distance from the loading point (mid-height of top
block) to the base of the wall, and the wall length was 1.2 and 1.5, respectively,
for the two groups of specimens. The main features of the test specimens are summarized
in Table 3-1.
3.2.2 Design of Test Specimens
The main design parameters of the test units were the shear stress demand and type of
cement-based material. Moderate intensity shear stress reversals were
the target for Specimens S1, S2, S6, S7, and S8, whereas Specimens S4, S5, S9 and S10
were designed for a higher shear stress demand . Thus, the longitudinal
and transverse reinforcement in each wall was chosen such that the target shear stress
level could be attained without a premature shear failure. It should be noted that a
Specimen S3, originally planned as part of the experimental program, was not tested,
which is the reason for skipping Specimen S3 in the list of test specimens.
The walls constructed with regular reinforced concrete (Specimens S1, S4, S6 and S9)
were designed following the seismic provisions in Chapter 21 of the 2005 ACI Code (318
ACI Committee, 2005). However, the design of the RC specimens also complied with the
provisions of the 2008 ACI Code since the only difference in the two editions of the code
is related to a relaxation in the maximum allowable spacing of the confinement
reinforcement in the wall edges, as discussed in Section 2.2.3. For each wall, the main
longitudinal wall reinforcement was concentrated in the wall edges and web horizontal
and vertical distributed reinforcement was also provided. All longitudinal bars were
43
continued along the wall height and were fully anchored in the base block by means of a
standard hook. Because large inelastic deflections were expected to be imposed on the
test walls, special boundary elements were provided in all the reinforced concrete walls,
as will be discussed later.
The configuration of the reinforcement for the HPFRC specimens (Specimens S2, S5, S7,
S8 and S10) followed the same basic layout as their companion reinforced concrete walls.
The longitudinal wall reinforcement was chosen such that the shear stress demand would
be approximately the same as that in the companion RC specimen. The ACI Code
provisions for the web distributed reinforcement and the confining reinforcement in the
boundary elements were not explicitly followed in the design of the HPFRC specimens,
as a major goal in this study was the evaluation of a possible relaxation in the
reinforcement configuration.
Because of the construction sequence, which was meant to simulate that in real
construction, a cold joint existed between the specimen base block and the bottom section
of the wall. In the case of conventional reinforced concrete construction, the effect of this
cold joint can be minimized by proper roughening of the surface of the footing. For the
HPFRC walls, on the other hand, the cold joint is more critical because the joint section
could be significantly weaker than the adjacent sections above the foundation due to the
lack of fibers bridging the base-wall interface. Furthermore, because of the excellent
bond between reinforcement and HPFRC materials (Parra et al., 2005; Chao et al., 2007),
the longitudinal reinforcement would likely yield only in the region close to the cold
joint. This concentration of yielding at the base of the wall could ultimately result in a
sliding shear failure or even fracture of the reinforcement with a detrimental effect on
wall displacement capacity. Thus, dowel bars were added in most HPFRC walls, as it will
discussed in Section 3.2.3, to strengthen the wall-foundation interface and prevent
concentration of inelastic rotations at this cold joint.
44
The maximum flexural strength at the base of each wall, , was predicted using a
sectional analysis and assuming plane sections remain plane after loading. Both the
reinforcement concentrated in the boundary elements and the distributed web
reinforcement were included in the strength computations. The concrete compressive
strength, , was assumed to be equal to 5000 psi for the regular concrete and the HPFRC
mixtures. A 1.25 multiplier was applied to the nominal yield strength of the steel, , to
account for material overstrength and strain hardening, as specified in Chapter 21 of the
ACI Code. It was also assumed that the dowel bars, when used in the HPFRC specimens,
could develop 50% of their yield strength. The maximum base shear, , was
computed by dividing the predicted maximum flexural strength by the shear span
length, , as shown in Eq. (3-1).
(3-1)
The wall transverse reinforcement (i.e. the web horizontal distributed reinforcement) was
chosen such that the shear demand, based on the predicted maximum flexural strength,
would not exceed the nominal shear strength according to the ACI Code. The only
exception was the design of Specimens S7 and S8, tested by Kim and Parra (2003), in
which the wall transverse reinforcement was selected such that the nominal flexural
strength of the wall would be approximately 1.2 times its assumed shear strength. The
vertical web reinforcement ratio was chosen to be equal to the horizontal reinforcement
ratio, as required by the ACI Code for structural walls with a height-to-length ratio less
than 2.0.
For the reinforced concrete walls, the nominal shear strength, , was calculated from
Section 21.7.4.1 of the 2005 ACI Code, as follows:
(3-2)
45
where the contribution of “concrete” to wall shear strength is equal to (psi) for
structural walls with a height-to-length ratio less than 2.0. The shear strength of the
HPFRC specimens, on the other hand, was estimated assuming an increased contribution
from the cementitious matrix because of the strain-hardening properties of the HPFRC
material. Chompreda and Parra (2005), based on tests of HPFRC beams under
displacement reversals, concluded that a shear strength of (psi) represented a
lower limit for the shear resistance of HPFRC flexural members with no transverse
reinforcement, regardless of the rotation demand. However, for the HPFRC low-rise
walls tested in this study, the “fiber-concrete” contribution to shear strength was assumed
to be (psi) because of the beneficial effect of arch action on the shear resistance of
low-rise walls. The maximum base shear and the nominal shear strength values used for
the design of the specimens are given in Table 3-2.
Shear transfer at the base of the RC and HPFRC walls was checked based on Section
11.6 of the 2005 ACI Code, as required for “interfaces between two concretes cast at
different times”. The nominal shear strength for shear transfer, , based on a shear-
friction model, is given by the following equation:
(3-3)
where is the area of the shear-friction reinforcement perpendicular to the shear-
friction plane, i.e. the total vertical reinforcement crossing the wall base, is the yield
strength of the shear-friction reinforcement (with a maximum value of 60,000 psi) and
is a coefficient of friction in accordance with 2005 ACI Code Section 11.6.4.3. In the
case of the RC walls in this study, the value of was taken equal to 0.6 (“concrete placed
against hardened concrete not intentionally roughened”). In addition, the nominal
strength for shear-transfer cannot exceed the smallest of (equal to 160 kips for
) or (equal to 128 kips), as required in ACI Code Section 11.6.5.
Table 3-3 lists the values of for shear transfer at the wall base for all the specimens. It
can be observed that for all the RC walls, the nominal strength for shear-transfer
46
exceeded the maximum base shear, , and thus, no additional dowel reinforcement
had to be provided based on the ACI Code provisions. In the case of the HPFRC walls,
dowel reinforcement was added because, as mentioned before, the cold joint was
considered to be more critical than in the RC companion specimens.
The check for special boundary elements for the RC walls was performed based on the
“stress check” of Chapter 21 of the 2005 ACI Code (Section 21.9.6.3). The stress-based
check is considered more appropriate than the displacement-based check for use in low-
rise walls such as those tested in this study. Table 3-4 lists the value of the extreme fiber
compressive stress corresponding to the maximum flexural strength at the wall base for
all test specimens. A linear elastic model and gross section properties were considered, as
required by the ACI Code. The stress values for the HPFRC walls are also included in the
table for comparison purposes, even though confinement reinforcement was eliminated or
significantly relaxed. It can be observed that in the RC walls, the maximum compressive
stress greatly exceeded the limit of (equal to 1000 psi for ) in all
cases. As a result, special boundary elements had to be provided in the RC walls. It
should also be noted that performing the check based on the displacement-based
approach would have also resulted in the same conclusion.
The bottom and top beam in each specimen were designed to remain elastic thought the
test. The bottom block was designed using a standard 2-D strut-and-tie model. The
bottom block had the same dimensions in all the specimens, and slightly increased
longitudinal reinforcement ratio for the specimens tested under higher shear stress. The
dimensions and the reinforcement of the top block were chosen so that the load could be
safely transferred to the specimen and to accommodate the connection with the hydraulic
actuator. The dimensions and reinforcing details for the bottom and top blocks are
provided in Figs. 3-2 and 3-3.
47
3.2.3 Reinforcing Details of Test Specimens
The reinforcing details for all the specimens are listed in Table 3-5 and the reinforcement
configuration for each specimen is shown in Figs. 3-4 through 3-13. In the following, a
summary of the design details for all the specimens is given.
3.2.3.1 Specimens with Shear Span-to-Length Ratio of 1.2
Specimen S1 was constructed with regular concrete and designed according to the
seismic provisions of the 2005 ACI Building Code (ACI Committee 318, 2005). The wall
longitudinal reinforcement was selected such that an average shear stress demand in the
range of (psi) to (psi) would be imposed on the wall. The purpose of this test
was to obtain a representative behavior of modern reinforced concrete walls with a shear
span-to-length ratio close to 1.2 when subjected to shear stress reversals of moderate
intensity.
The wall main longitudinal reinforcement in Specimen S1 consisted of 4 No. 4 (0.5 in.
diameter) Grade 60 bars in each boundary region, placed in two layers, continuous
through the wall and fully anchored in the base beam. This amount of wall main
longitudinal reinforcement translated into a wall boundary reinforcement ratio, , of
5.0% according to Chapter 21 of the ACI Code, and a tension reinforcement ratio, , of
0.53% , where is the area of main longitudinal reinforcement and is the
wall thickness). Two layers of smooth No. 2 (0.25 in. diameter) bars spaced at 3.5 in. on
center were used as web horizontal reinforcement, resulting in a web reinforcement ratio
of 0.71%. The web vertical reinforcement ratio was also chosen equal to 0.71%. The
confining reinforcement in the wall boundary regions was provided through closed hoops
made of 0.162 in. diameter smooth wire spaced at 1.0 in. The required confinement
reinforcement ratio, rather than the maximum allowed spacing, governed the design. For
a concrete compressive strength of 5000 psi and wire reinforcement yield strength of 29
ksi, the hoop spacing, as calculated from Equation (2-3), was equal to 0.9 in. However,
for ease of construction, it was decided to use a spacing of 1.0 in. since this would not
48
compromise the behavior of the specimen. The reinforcing details for the wall of
Specimen S1 are given in Fig. 3-4.
In the wall of Specimen S2, an HPFRC material containing a 2.0% volume fraction of
hooked steel fibers was used. This specimen was the first wall in this investigation
constructed with a fiber cementitious material and the HPFRC material chosen was the
same as that used in Specimen S7 tested earlier by Kim and Parra (2003). Information on
HPFRC mixture used in Specimen S2 is given in Section 3.3.1 and Tables 3-6 and 3-7.
The main longitudinal reinforcement at the wall edges was the same as that in the control
RC Specimen S1 such that the peak shear stress demand would be approximately the
same in the two specimens. However, a possible relaxation of the web horizontal and
vertical reinforcement was investigated in Specimen S2. Two layers of smooth No. 2
bars, spaced at 8.0 in. on center, were chosen for the web reinforcement, which
corresponded to a horizontal and vertical reinforcement ratio of 0.31%. This ratio is less
than one half of that used in Specimen S1 and is close to the minimum reinforcing ratio
of 0.25% specified in the ACI Code. Thus, the shear strength provided by the horizontal
web reinforcement, assuming a vertical projection of the critical diagonal crack equal to
, represented less than 50% of the expected shear stress demand and was estimated to
be in the order of (psi).
The confining reinforcement in the boundary region of Specimen S2 was completely
eliminated and as a result, the transverse reinforcement at the wall edges consisted only
of the extension of the web horizontal reinforcement, terminated with a 135 degree hook
at one end and a 90 degree hook at the other end. The elimination of the special confining
reinforcement was decided based on the promising results obtained from the earlier study
by Kim and Parra (2003) and allowed the evaluation of the ability of the HPFRC material
to sustain large compressive strain demands and provide confinement to the wall
longitudinal reinforcement. Further, this allowed an evaluation of whether HPFRC
materials can provide sufficient lateral support to prevent buckling of the longitudinal
bars in the wall boundary region.
49
As discussed earlier, sliding shear failure was considered as a possible failure mechanism
in the HPFRC walls because of the presence of the cold joint at the wall base (see Section
3.2.2). However, given the low wall aspect ratio, it was assumed that concentrated
flexural deformations at the wall base would likely not be large enough to result into a
sliding shear failure and thus, no dowel reinforcement was placed at the wall base of
Specimen S2. The lack of dowel reinforcement in Specimen S2 would also allow the
evaluation of the influence of the cold joint on the behavior of HPFRC low-rise walls.
Reinforcing details for Specimen S2 are provided in Fig. 3-5.
Specimens S4 (RC) and S5 (HPFRC) had the same geometry as that of Specimens S1 and
S2, but were designed with an increased longitudinal reinforcement ratio in the boundary
regions such that a higher shear stress demand in the range of (psi) to
(psi) would be imposed on the walls. The testing of these two specimens would thus
allow the evaluation of the influence of shear stress demand on the behavior of RC and
HPFRC walls when subjected to displacements reversals.
Specimen S4 was constructed with regular concrete. Two No. 6 and 2 No. 5 Grade 60
bars were used in each boundary region of the wall, which translated into a wall boundary
reinforcement ratio of 9.4% and a wall tension reinforcement ratio of 1.0%. No dowel
bars were used to strengthen the wall-foundation interface. A deformed wire was chosen
for the web distributed reinforcement to better simulate the behavior of walls with
standard deformed bars (more information about the properties of these bars is given in
Section 3.3.3). It should be mentioned that these small diameter deformed bars were
difficult to find and thus, they were not available for use in all the wall specimens. Two
layers of D5 wire (area = 0.05 in.2
) at 3.0 in. on center were used as horizontal and
vertical wall reinforcement in Specimen S4, which translated into a web reinforcing ratio
of 0.83%. The confining reinforcement in the boundary regions was the same as that in
RC Specimen S1. The reinforcement layout for Specimen S4 is given in Fig. 3-6.
50
The wall in Specimen S5 was constructed with a relatively new type of HPFRC material.
A self-consolidating, high performance fiber reinforced concrete with a 1.5% volume
fraction of high-strength (330 ksi) hooked steel fibers was chosen in order to facilitate
concrete casting (Liao et al., 2007). This HPFRC mixture contains coarse aggregate (
in. maximum size), which makes the material more attractive for large-scale applications.
Information on this mixture will be given in Section 3.3.1
As it will be discussed in Chapter 4, sliding shear deformations played a significant role
in the behavior of HPFRC Specimen S2, which was constructed without the addition of
dowel reinforcement at the wall-foundation interface. Thus, dowel bars were provided at
the wall base of Specimen S5 in order to strengthen the wall-base block interface and
force flexural yielding to primarily occur above the cold joint. In order to prevent the
occurrence of a predominant flexural crack caused at the termination of the dowel bars,
these dowel bars were extended, debonded, beyond the wall plastic hinge region, as
shown in Fig. 3-7. A close-up photo of the dowel bars and the debonded regions is shown
in Fig. 3-8. The use of diagonal bars in the web of the concrete walls, even though it has
been generally proven effective to prevent a sliding shear failures was considered to be
difficult to implement in practice and thus, it was ruled out as an alternative to the use of
dowel reinforcement.
The main vertical wall reinforcement in HPFRC Specimen S5 consisted of 4 No. 5,
Grade 60 bars in each boundary region and two layers of 4 No. 4 dowel bars, distributed
as shown in Fig. 3-9. The spacing of the wall distributed horizontal and vertical
reinforcement was relaxed compared to that in Specimen S4. D5 wire reinforcement was
spaced at 4.0 in. on center, corresponding to a horizontal and vertical reinforcing ratio of
0.63%. Based on the preliminary results of the tests of Specimens S7 and S8 (Kim and
Parra, 2003) and Specimen S2, the complete elimination of special confining
reinforcement in the wall boundary regions through the use of HPFRC seemed a feasible
design solution. However, given the high intensity of the stress demand that would be
imposed on Specimen S5, some confining reinforcement was used. Single hoops made of
51
0.162 in. diameter wire at 4.0 in. spacing was provided in the wall boundary regions,
which corresponded only to one-fourth of the confinement reinforcement in the
companion RC Specimen S4.
3.2.3.2 Specimens with Shear Span-to-Length Ratio of 1.5
Specimen S6 was designed as a conventional reinforced concrete structural wall for an
average shear stress demand between (psi) and (psi). This specimen
represented a control specimen for the HPFRC low-rise walls with a shear span-to-length
ratio of 1.5 and the shear stress level was chosen to be approximately equal to the shear
stress level of Specimens S7 and S8, which were previously tested by Kim and Parra
(2003). The wall was designed based on the provisions of the 2005 ACI Code, as for RC
Specimen S1. Main vertical tension reinforcement ratio was approximately 1.0%,
consisting of two No. 5 and two No. 6 bars. For the vertical and horizontal web
reinforcement, smooth No. 2 bars, spaced at 3.5 in. on center, were used, which translated
into a reinforcement ratio of 0.71%. The confinement reinforcement in the boundary
regions consisted of singe hoops made out of a 0.162 in. diameter wire, spaced at 1.0 in.
Reinforcement detailing for Specimen S6 is shown in Fig. 3-10.
Specimens S7 and S8 were designed and tested by Kim and Parra (2003) and, to the
writer’s knowledge, were the first HPFRC low-rise walls tested under displacement
reversals. Specimens S7 and S8 were constructed with an HPFRC material containing
hooked steel fibers and ultra-high molecular weight polyethylene (Spectra) fibers,
respectively. The reinforcing bars in these two specimens were placed in a single layer,
given the lack of experience at the time in casting HPFRC in these elements. It was
argued that the use of one layer of reinforcement would not compromise the behavior of
the walls because of the beneficial effect of using a ductile concrete material in tension.
However, casting of the walls in Specimens S7 and S8 did not present any significant
challenge and thus, it was decided to use two layers of reinforcement in all the HPFRC
specimens designed for this study.
52
The longitudinal reinforcement in Specimen S7 and S8 consisted of 3 No. 7 bars at each
edge, which corresponded to a tension reinforcement ratio of 1.1%, while 4 No. 5 bars
were added as dowel reinforcement. Smooth No. 2 bars at 10 in. and 6.0 in. on center
were provided as distributed horizontal and vertical wall reinforcement, respectively. No
special boundary confinement reinforcement was used, as in HPFRC Specimen S2. The
reinforcing details for HPFRC Specimens S7 and S8 are shown in Fig. 3-11.
The last two specimens (S9 and S10) were designed for a high shear stress demand
(between (psi) and (psi)). For Specimen S9, which was constructed with
regular concrete, 2 No. 7 and 2 No. 6 bars were used as the main flexural reinforcement
based on the target shear stress level. The chosen bars corresponded to a boundary
reinforcement ratio of 13% and a tension reinforcement ratio of 1.4%. The wall
horizontal and vertical distributed reinforcement was provided in the form of crimped
wire (more information in Section 3.3.2). Two layers of D4 crimped wire (area=0.04 in.2
For Specimen S10, 4 No. 6 bars were used as the wall main longitudinal reinforcement,
which along with the two layers of 4 No. 4 dowel bars, resulted in a moment capacity at
the wall base approximately equal to that of the companion RC Specimen S9. The upper
end of the dowel bars was also debonded, as in Specimen S5. The web distributed
reinforcement (D4 wire) was spaced at 4.0 in., resulting in a horizontal and vertical
distributed reinforcement ratio of 0.5%. For Specimen S5, single hoops (0.162 in.
diameter) at 4.0 in. spacing were provided in each boundary element. Fig. 3-13 provides
the details of the reinforcement for this specimen.
)
at 3.0 in. on center were provided, which translated into a horizontal and vertical
distributed reinforcement ratio of 0.67%. The boundary confining reinforcement was the
same as that in all the reinforced concrete specimens (0.162 in. diameter wire at 1.0 in.
spacing). The elevation and cross-section of Specimen S9 can be seen in Fig. 3-12.
53
3.3 MATERIALS USED IN THE STUDY
3.3.1 Concrete Mixtures
3.3.1.1 Mixing Proportions
The concrete used for the wall in the specimens constructed with conventional reinforced
concrete (Specimens S1, S4, S6 and S9) was mixed in the Structural Engineering
Laboratory at the University of Michigan. The proportions by weight of this mixture were
1:1.55:1.45:0.48 (cement: sand: coarse aggregate: water). Type III cement (high early
strength) was used and the coarse aggregate consisted of crushed limestone with 1/2 in.
maximum aggregate size. The sand used was 2NS sand, which according to Section 902
of the 2003 Standard Specifications for Construction of the Michigan Department of
Transportation (Aggregate Div., Levy Corporate, Dec. 2008, http://www.edwclevy.com)
refers to natural sand with particles sized from 3/8 in. to mesh #200 (diameter of 0.00295
in.). A rheobuild 1000 high-range water reducing admixture was used in some cases to
achieve adequate workability.
The fiber reinforced mortar mixture used for HPFRC Specimen S2 was the same as that
used in previous investigations on the seismic behavior of HPFRC structural members
(for example Canbolat et al., 2005), and it was also used in Specimen S7 tested by Kim
and Parra (2003). The mortar was mixed in the Structural Engineering Laboratory with
proportions by weight of 1:2:0.48:0.20 for Type III cement, #16 silica sand, water, and
class C fly ash. The silica sand is a product referred to as “Flint Silica #16”,
manufactured by U.S. Silica Company, with particles sized from mesh #20 (diameter of
0.03346 in.) to mesh #140 (diameter of 0.00417 in.). Regular strength (160 ksi) hooked
steel fibers, 1.2 in. long and 0.022 in. diameter (Bekaert ZP 305) in a volume fraction of
2.0%, were used in this mixture, denoted as HPFRC-SH mixture. For the wall of
Specimen S8 (Kim and Parra, 2003), the mixture proportions by weight of the fiber
cementitious material were 1:1:0.5:0.15 (type III cement: silica sand: water: class C fly
ash). Ultra high molecular weight polyethylene (Spectra) fibers in a volume fraction of
1.5% were used in this mixture, which was denoted as HPFRC-PE mixture.
54
The mixture used for HPFRC Specimens S5 and S10 is one of a series of self-
consolidating HPFRC mixtures developed at the University of Michigan for seismic
applications (Liao et al., 2007). This mixture was chosen such as to investigate its use in
structural applications and to ease the casting of the wall specimens, given the small
thickness of the walls (4 in.). The mixing ratio of this HPFRC material by weight was
1:2.2:1.2:0.8:0:885:0.005:0.038 for Type III cement, #16 Silica sand, coarse aggregate,
water, class C fly ash, superplasticizer, and a viscosity modifying admixture (VMA). The
coarse aggregate consisted of solid crushed limestone with a maximum size of in.
The superplasticizer used was a polycarboxylate-based plasticizer and the VMA agent
was basically used to enhance the viscosity and reduce fiber segregation in the presence
of higher water-to-cementitious ratios. A 1.5% volume fraction of 1.2 in. long, 0.015 in.
diameter, high-strength (330 ksi) hooked steel fibers was used in this mix denoted as
SCHPFRC mixture.
The bottom and top block of the specimens were constructed with regular concrete. The
concrete mixture for the bottom block for all the specimens was provided by a local
ready-mix concrete supplier, whereas the mixture for the top block was either delivered
by a ready-mix concrete supplier or prepared in the Structural Engineering Laboratory.
The ready-mix concrete was specified as a 4000 psi compressive strength mixture, with
3/8 in. maximum aggregate size and 6 in. slump. The regular concrete mixed in the
laboratory, on the other hand, had the same proportions as those for the regular concrete
used in the walls of Specimens S1, S4, S6 and S9. Table 3-6 lists the details for the
different mixtures used in this study. It should be mentioned that the compressive
strength of the ready-mix concrete used in the bottom block of Specimen S10 was less
than the specified strength of 4000 psi because the mixture had a substantially higher
water-to-cement ratio than the ratio originally specified in the mixture due to an error of
the concrete supplier.
55
3.3.1.2 Mixing Process
The regular concrete mixture mix was prepared in the laboratory in either a 5 or a 1.5
cubic feet capacity mixer (Fig. 3-14). The mixing process followed standard practice for
mixing regular concrete. Due to the capacity of the mixers and the required volume of
concrete, several batches had to be prepared to complete the casting for each of the walls.
The 1.5 cubic feet capacity mixer was also used for the HPFRC material used in the wall
of Specimen S2. The fibers were added last to the mixer. Although concrete slump was
not measured before the fibers were added, it was obvious that the workability of the
mixture was affected. However, the casting of the wall was performed without significant
problems.
The mixing procedure and mixing time for the self-consolidating HPFRC mix used in
Specimens S5 and S10 followed the recommendations by Liao et al. (2007). The mixing
procedure, including the sequence by which different materials are placed in the mixer,
and the mixing time are critical to successfully achieve a self-consolidating concrete
mixture. For the mixture used in this study, the cement, fly ash and sand had first to be
dry-mixed for 30 seconds and then the pre-mixed liquid (water, superplasticizer and
VMA) was added slowly such as to limit the formation of lumps in the paste. The coarse
aggregate was then added and after 2 minutes, the steel fibers were added slowly to the
mixture. The mixing process was continued for approximately 3 minutes after the
addition of fibers was completed.
3.3.2 Fibers
Three types of fibers, two made of steel and one made out of ultra high molecular weight
polyethylene, were evaluated in this study and their properties are listed in Table 3-7. The
steel fibers had a circular cross-section with their ends bent such as to create a hook and
enhance the mechanical bond with the concrete matrix (Fig. 3-15(a)). These fibers are
commercially available through Bekaert S.A., Belgium, by the name Dramix. The first
Dramix fiber used is referred to as ZP305 fiber. This fiber has been used in many
56
applications, such as slabs, retaining walls, precast members, sprayed concrete, and
pavements. Dramix ZP305 fibers are 1.2 in. long with a diameter of 0.022 in. The tensile
strength of the fiber, as reported by the manufacturer, is in the range of 160 ksi to 200 ksi,
with an elastic modulus of 29,000 ksi. These fibers were used in Specimens S2 and S7.
The other Dramix fiber used in this study is referred to as RC-80/30-BP fiber. It is a high-
strength hooked steel fiber, 1.2 in. long, and with a diameter of 0.015 in. The specified
tensile strength of this fiber was 335 ksi (2300 MPa). This high-strength hooked steel
fiber was used in Specimens S5 and S10.
Ultrahigh molecular weight polyethylene (Spectra) fibers were used in Specimen S8 (Fig.
3-15(b)). Spectra fibers are widely used in fiber reinforced polymers for the aerospace
industry. The fibers had a length of 1.5 in. and a diameter of 0.0015 in. The fiber tensile
strength and elastic modulus reported by the manufacturer were 375 ksi and 17,000 ksi,
respectively.
The fibers used in this experimental program were selected on the basis of previous large-
scale tests conducted at the University of Michigan. Test results from direct tensile tests
on FRC (mortar) with Dramix ZP305 fibers were reported by Chompreda and Parra
(2005). They reported a tensile strain-hardening behavior in composites with a 2% fiber
volume fraction, while a strain-softening behavior with gradual strength decay was
reported for composites with a 1.5% fiber volume fraction. Further, the preliminary
results from the low-rise wall test (Specimen S7) by Kim and Parra (2003) showed great
potential for the application of these fibers in structural walls. The HPFRC mixture with
the Spectra fibers was reported to have maximum tension strength of approximately 0.51
ksi and an average peak strain of 2.0% (Kim and Parra, 2003). The Dramix RC-80/30-BP
fiber was used in combination with the self-consolidating HPFRC mixture described
above. As reported in the study by Liao et al. (2007), this self-consolidating mixture
57
exhibits a strain-hardening behavior in tension, up to a strain in the range of 0.25% to
0.5% with a peak stress of approximately 0.5 ksi.
3.3.3 Reinforcing Steel
In all the specimens, the deformed reinforcing bars (No. 4, 5, 6 and 7 bars) were made
out of Grade 60 steel. The No. 2 bars used in Specimens S1, S2, S6, S7 and S8 were
smooth bars because deformed No. 2 bars could not be obtained. These bars did not
conform with ASTM standards. Separate steel orders were made for the reinforcement
used in Specimens S1 and S2, S4 and S5, S6, S7 and S8, and S9 and S10.
For Specimens S9 and S10, a crimped wire (D4, area=0.04 in.2) was used for the wall
web reinforcement in order to enhance the bond between the reinforcement and the
matrix. The crimped wire was obtained from Milliken Steel Sales Ltd. in Canada and it
was basically a smooth wire that was driven through a crimping machine to create
indentations (Fig. 3-16(a)). The manufacturer reported that this material does not have a
yield plateau and rather exhibits a cold-formed steel behavior with a yield stress based on
the 0.2% offset method of about 90 ksi and an ultimate stress of about 96 ksi. A deformed
wire (D5, area=0.05 in.2
) that conforms to ASTM Standard A 496-02 “Standard
Specification for Steel Wire, Deformed, for Concrete Reinforcement” was used in
Specimens S4 and S5 because it was considered a better alternative to the previously used
crimped wire (Fig. 3-16(b)). This wire was obtained from Wire Products Inc. in Florida
and is described as a “positive deformation pattern” wire with a nominal yield stress of
75 ksi.
The boundary confining reinforcement for all the specimens was constructed from a
0.162 in. diameter smooth wire. The wire was a general purpose low carbon steel wire
that met the ASTM A853 requirements for coating only. This wire had a yield and
ultimate strength of 29 ksi and 47 ksi, respectively, based on test results from previous
58
studies (Chompreda and Parra, 2005). The wire was delivered in the form of a coil and
the hoops were prepared in the laboratory.
3.3.4 Material Testing
3.3.4.1 Concrete and HPFRC Materials
The average compressive strength of the concrete and HPFRC mixtures was determined
through compressive tests of in. cylinders. For each batch of material prepared in
the laboratory and for all ready-mix concrete delivered, six cylinders were prepared.
Three cylinders were tested at 28 days and the other three were used to record the
concrete strength one day after the test. Tests were conducted using an Instron testing
machine operated under displacement control. The average compressive strength
obtained from the cylinder tests performed one day after the test day are listed in Table 3-
8.
In addition to cylinder tests for evaluation of compressive strength, beam specimens with
dimension of in. were prepared for the HPFRC material used in Specimens
S5 and S10. Five beams were cast for Specimen S5, three from the first batch and two
from the second batch. For Specimen S10, three beam specimens were made from each
of the two batches. All beams were tested under third-point loading with an 18 in. span
length, according to ASTM 1609-05 (Fig. 3-17). Net midspan deflections were measured
through two linear potentiometers with a 0.1 in. stroke length connected to an
instrumentation frame, as shown in Fig. 3-17. Key results from the tests are given in
Table 3-9. First peak load (cracking load) is defined, according to ASTM 1609-05
(Section 10.2), as the load value at the first point on the load versus deflection curve
where the tangent slope is zero. Figs. 3-18 and 3-19 show the load versus deflection
response for the beam specimens tested for Specimens S5 and S10, respectively.
Strengths at deflection levels equal to 0.03 in. (span length/300) and 0.12 in. (span
length/150) are provided in Table 3-9. The tests were terminated after a midspan
deflection of 0.12 in. was reached, as required by ASTM 1609-05 (Section 9.5).
59
Kim and Parra (2003) reported on results from tension tests of the HPFRC materials used
in Specimens S7 and S8. Based on the tensile stress-strain response of the HPFRC
material with hooked steel fibers and Spectra fibers, the first cracking strength was
approximately 0.43 ksi both materials. The HPFRC material with hooked steel fibers
(ZP305) showed a pea tensile stress of 0.60 ksi at a strain of approximately 0.5%. On the
other hand, the peak tensile stress and corresponding strain for the HPFRC material with
Spectra fibers were 0.51 ksi and 2%, respectively.
3.3.4.2 Reinforcing Steel
Samples of the reinforcing steel used to construct the wall of the specimens were tested
under direct tension to determine their yield and ultimate strength. For each bar size in
each shipment, two or three 24-in. long coupons were randomly selected and tested. The
results are summarized in Table 3-10. The stress-strain curve for the D4 wire, as obtained
from direct tension tests, is shown in Fig. 3-20.
3.4 CONSTRUCTION OF SPECIMENS
All the specimens were constructed in the Structural Engineering Laboratory at the
University of Michigan. To ensure realistic construction-site conditions, all test units
were built in the fully upright position. This construction process was deemed to be
necessary to ensure a realistic distribution and orientation of the fibers in the HPFRC
walls. However, the casting of the specimens was somewhat challenging in some cases
because of the small wall thickness (4 in.). The construction sequence is briefly presented
below.
First, the reinforcement of the base block was tied and the cage was placed in a wooden
formwork (Fig. 3-21). PVC pipes were embedded in the formwork for the placement of
the high strength threaded rods that were used to connect the specimen to the strong floor.
Then, the wall longitudinal bars, which were continuous over the wall height, were
assembled and concrete was poured in the base block using ready-mix concrete provided
by a local supplier. Fig. 3-22 shows a specimen ready for casting of the base block.
60
Subsequently, the wall transverse reinforcement above the base block was placed (Fig. 3-
23), the formwork of the wall was put in place (Fig. 3-24), and the wall concrete was cast
in one lift. In Fig. 3-25, Specimen S4 is shown after the completion of the wall casting
and the removal of the formwork. Finally, the formwork for the top beam was put in
place, the top block reinforcement was assembled (Fig. 3-26), and regular concrete was
poured. Concrete cylinders were prepared for every batch of concrete prepared in the
laboratory and for every ready-mix concrete delivery.
After each concrete casting, the exposed concrete was covered with plastic sheets for 2-3
days. The forms were removed about one week after casting. Once the specimen
construction was completed (Fig. 3-27), the specimen was lifted with the crane and
placed into the test set up. Concrete material samples were also covered with plastic
sheets for approximately two days, at which point they were demolded and placed in a
water tank until testing.
As discussed previously, the specimen casting sequence resulted in a cold joint between
the specimen base block and the bottom section of the wall. For the regular concrete
specimens and HPFRC Specimen S2 the cold joint was left unreinforced. In the other
HPFRC specimens, dowel bars were used to strengthen the wall-base interface and force
inelastic deformations to occur within the HPFRC wall.
Difficulties were encountered during the casting of the wall of Specimen S10, which was
the first wall in the study to be constructed with the self-consolidating HPFRC mixture. A
self-consolidating mixture could not be achieved for this specimen. Further, the mixture
showed poor workability during casting and significant vibration was necessary to make
sure that the material would flow throughout the wall. However, the removal of the
formwork revealed air voids in the wall, there were generally away from the expected
plastic hinge region. A grout mixture was used to patch those regions and the behavior of
the specimen was not compromised, as was evident during the test.
61
3.5 SPECIMENS INSTRUMENTION
Strains in the reinforcement were measured using electrical resistance strain gauges
attached to the reinforcing bars at several locations. The location and label for the strain
gauges placed on the wall reinforcing bars are shown in Figs. A-1 to A-8 in Appendix A.
One face of each specimen was instrumented with linear potentiometers positioned
vertically, horizontally and diagonally to monitor average shear strain distortions and
rotations. Vertical potentiometers were also placed adjacent to both side edges of the
walls to measure rotations at the wall base. Rigid body horizontal displacement (sliding)
of the bottom block and sliding of the wall with respect to the base block were recorded
through potentiometers attached to a fixed location. The rotation of the bottom and top
blocks was monitored using clinometers. A typical arrangement of the potentiometers and
inclinometers is shown in Figs. 3-28 and 3-29. A load cell and a Linear Variable
Differential Tranformer (LVDT) were used to monitor the applied load and lateral
displacement of the actuator, respectively. The readings from all the instruments were
collected simultaneously through a data acquisition system at a sampling rate of 2 Hz.
An Optotrak Certus motion capture system, manufactured by NDI, Canada, was also used
during the testing of Specimens S4, S5, S9 and S10. Optotrak is a non-contact motion
measurement system that tracks the position in space of small sensors. Only one position
sensor is required to determine the 3D location of the point to which the sensor is applied.
In this investigation, the sensors were attached to one face of the specimen,
forming grid, as can be seen in Fig. 3-30. Using the recorded coordinates of
the sensors during the test, average strains and rotations were determined at various
locations. For the specimens where both potentiometers and Optotrak markers were used,
it was possible to compare the results from the two instrumentation procedures and
conclude on their overall accuracy. Photos of the instrumentation schemes are shown in
Figs. 3-31 and 3-32.
62
3.6 TEST SET UP AND TEST PROCEDURE
All the specimens were constructed in an area adjacent to the testing space in the
Structural Engineering Laboratory at the University of Michigan and were then moved
into the test location using an overhead crane. The specimens were anchored to the
laboratory strong floor through eight 1-1/2 in. diameter threaded rods. Liquid grout
forming an approximately 1/2 in. thick layer was cast between the top surface of the
bottom block and the 1-1/4 in. thick steel bearing plates connected to the threaded rods.
The specimens were also braced laterally at the top block to restrain out-of-plane
movements, as shown in Fig. 3-33. Subsequently, the external instrumentation was
placed and shortly before the test the horizontal hydraulic actuator was connected to the
strong wall at the mid-depth of the top block. A specimen ready for testing is shown in
Fig. 3-34.
A 100-kip hydraulic actuator with a ±15 in. stroke was used for the application of lateral
displacements for the specimens designed for moderate shear stress demands, (i.e.
Specimens S1, S2 and S6). However, for the specimens where high shear stresses were
expected, (i.e. Specimens S4, S4, S9 and S10), a 300-kip hydraulic actuator with an ±8
in. stroke was used. The typical test set-up is shown in Fig. 3-35.
The specimens were subjected to quasi-static reversed cyclic displacements, with the
peak displacement at a given cycle ranging from 0.125% drift to 3.0% drift. Drift was
calculated as the lateral displacement at mid-depth of the top block in relation to the top
of the base block divided by the initial distance between those two sections. Every
displacement cycle up to 2.0% drift was performed twice to evaluate any decrease in
strength and stiffness with repeated displacement cycles. The loading scheme used in this
study was the same used for Specimens S7 and S8 by Kim and Parra (2003), allowing the
test results to be compared with existing data. However, it should be mentioned that there
is no widely accepted reversed cyclic loading scheme for RC members and it has been
reported that the loading scheme can have a significant effect on the behavior and
ductility of RC members (Lehman et al., 2004; Matamoros and Sozen, 2003).
63
The target lateral displacement history is shown in Fig. 3-36. Ideally, the specimen would
be subjected to this drift history. During the test, the applied drift was corrected to
account for the sliding of the base block through the use of a horizontal potentiometer
attached to the base block (Figs. 3-28 and 3-29). The measured drift was further
corrected, after the test, to account for the rotation of the bottom block, as will be
described in Section 4.1. Drifts reported throughout this report are the corrected
(“actual”) drifts.
64
CHAPTER 4
EXPERIMENTAL RESULTS
4.1 DEFINITIONS
Before the test results are presented, some basic terms are first defined. This section
describes the calculation of average shear stress, wall drift, shear strains, rotations along
the wall height, and strains, including principal strains and directions.
4.1.1 Average Shear Stress
Average shear stress, , was obtained by dividing the applied lateral load, , by the
product of the wall length, , and thickness, , i.e. the wall cross sectional area, as
follows:
(4-1)
The applied lateral load represents the load cell reading from the hydraulic actuator.
In this report, shear stress is often expressed in multiples of in psi to facilite the
comparison with the shear strength equations given in the ACI Building Code. For
example, as discussed in Section 2.2.4, the shear strength attributed to concrete for
seismic design of low-rise walls is (psi), whereas the upper
65
strength limit is (psi). The normalization of the magnitude of the shear stress also
allows for an easy comparison of the shear stresses imposed on all the test specimens.
4.1.2 Drift
Drift is defined as the ratio between the lateral displacement of the wall and shear span:
(4-2)
where is the lateral displacement at the mid-depth of the top block and is the shear
span length, defined as the distance from the base of the wall to the mid-depth of the top
block.
The lateral displacement of the wall was obtained after correcting the displacement
applied through the actuator to account for rigid body displacements (rotation and slip) of
the bottom beam. The bottom beam rigid body displacements were measured with the use
of inclinometer CL1 and potentiometer P11, shown in Figs. 3-28 and 3-29. Thus, the
lateral displacement of the wall was calculated as follows (Fig. 4-1):
(4-3)
where, (in.) is the lateral displacement of the actuator, monitored through a Linear
Variable Differential Tranducer (LVDT), (in.) is the horizontral movement obtained
from potentiometer P11 attached to the base beam, (in.) is the elevation of
potentiometer P11 with repect to the laboratory strong floor, (rad) is the base block
rotation obtained from inclimometer CL1 attached to the base beam, and (in.) is the
elevation of the actuator with respect to the strong floor. The rigid body displacements of
the base block was also calculated using the data obtained from the Optotrak system
markers’ coordinates, when applicable, but no significant difference was found compared
to the measurements of the pontetiometer and inclinometer.
66
A correction to account for the flexibility in the loading fixtures also had to be
considered, as can be observed by comparing the displacement at the mid-depth of the
top block recorded from the actuator LVDT and the top block displacement as calculated
based on the lateral displacement and rotation of the top row of Optotrak markers (wall
portion above top row of markers was assumed to rotate as a rigid body)(). Fig. 4-2
shows a comparison plot of the top-block displacement in Specimen S5 obtained from the
two instrumentation methods (Optotrak markers system and actuator LVDT). Only the
load versus displacement response envelope for the first cycle at each drift level is plotted
in the figure. It can be seen that there is some difference in the top-block displacements,
especially in the negative (pulling) loading direction. The Optotrak system data gave
smaller displacements at each drift level and this can be attributed to the flexibility
associated to the loading apparatus, particularly to the deformation of the rods used to tie
the actuator to the top block (see Fig. 3-35). The difference in the displacements was
rather constant after the peak load was achieved for both loading directions. Very similar
plots were obtained for Specimens S4, S9 and S10 and as a result, the displacement
obtained from the Optotrak system, when availiable, was used to calculate the applied
lateral displacement of the wall in Eq. (4-3). For Specimens S1, S2, S6, S7 and S8, a
correction to account for the relaxation of the test set up could not be performed because
data from the Optotrak system was not availiable. Thus, the wall drift was calculated
from Eq. (4-3) based on the actuator displacement.
4.1.3 Shear Strain
The average shear strain (shear distortion) in the lower part of the wall was determined
using the data obtained through the diagonal potentiometers P1 and P2 or the Optotrak
system marker coordinates, when available (see Figs. 3-28 to 3-20). The average shear
strain can be calculated using the expression by Oesterle et al. (1976), based on the
change in length in the two diagonals:
(4-4)
67
where (rad) is the average shear strain and the rest of the variables are defined in Fig. 4-
3.
Eq. (4-4) is theoretically correct when the element experiences a constant curvature along
the height H. For the low-rise walls in this study, it can therefore be argued that the
values obtained for the diagonal lengths and were affected by the distribution of
the curvature along the height of the wall. However, the measured shear strain can be
corrected so that the shear distortion is not overestimated because of the flexural
deformations in the wall. A method to perform the correction was presented by Massone
and Wallace (2004), which required the readings from vertically, horizontally and
diagonally placed potentiometers. Even though the instrumentation scheme used in this
study included diagonal, vertical and horizontal potentiometers (see Fig. 3028 and Fig.
3029), the horizontal potentiometers did not work properly in some tests and thus, the
correction could not be performed in all the cases. Therefore, the shear strain was first
calculated for all the specimens using Eq. (4-4) and additionally, a more accurate
calculation was performed for the specimens where the Optotrak system was used. As
will be described in Section 4.1.6, it was possible to calculate the average shear strain for
each quadrilateral element in the marker grid using the Optotrak markers’ coordinates. As
shown in Fig. 4-4, the wall could then be divided in several horizontal strips along its
height. Each strip had a height of 5 in. and comprised seven quadrilateral elements. Given
the relatively small height of each strip, curvature was assumed to be constant in each
strip, allowing the shear strain to be estimated as the average shear strain of the seven
quadrilateral elements. This procedure allowed then the calculation of the shear strain
distribution, as well as the average shear strain in the walls over a region A
comparison plot for the two procedures will be shown and discussed in Section 4.5.
4.1.4 Flexural Rotations
Concentrated rotations at the bottom of the wall were calculated using the deformations
measured through the potentiometers attached to the sides of the wall, i.e. potentiometers
P7 through P10 (see Figs. 3-28 and 3-29). Using the same potentiometers, the rotation at
68
a height of 0.3h, where h refers to the wall height, could be also calculated. Rotations at
other sections along the wall height were also obtained using the inclinometers and the
data from the Optotrak markers.
4.1.5 Horizontal Slip at the Wall Base
The horizontal slip at the wall-base block interface was monitored with the use of
potentiometer P12 (see Figs. 3-28 and 3-29). The readings of the potentiometer were
corrected to account for the rigid body motion of the base block, as follows:
(4-5)
where (in.) is the slip at the cold joint, (in.) is the reading from potentiometer P12,
(rad) is the rotation of the bottom block, and (in.) is the elevation of potentiometer
P12 with respect to the laboratory strong floor. The slip was also calculated using the data
from the the Optotrak markers located at 4 in. above the wall base, resulting in similar
values. It should be mentioned that potentiometer P12 monitored the horizontal
displacement of the wall at approximately 3 in. from the base block. Thus, the
measurements were slighly affected by the deformation and rigid body rotation of the
wall in this region.
4.1.6 Calculation of Strain Field from Optotrak Data
Using the coordinates of the Optotrak markers, the average strains in the wall plane for
each quadrilateral element were calculated. The coordinates of the markers were first
transformed to a coordinate system in the plane of the wall (such that the x- and y-axis
defined the plane of the wall) in order to obtain the in-plane displacement of the markers.
With the displacements of the markers known, the average strains were calculated.
69
Consider a quadrilateral element deformed as shown in Fig. 4-5. If the coordinates and
displacements of all four nodes 1, 2, 3, and 4 are known, the average strains xε , yε and
xyγ can be calculated as follows:
(4-6)
(4-7)
(4-8)
where:
(4-9)
(4-10)
(4-11)
(4-12)
Once the strain field is available, the principal strains and directions are computed as follows:
(4-13)
(4-14)
(4-15)
70
The calculated shear strain in each quadrilateral element, , was also used to obtain the
average shear distortion in the wall, as discussed in Section 4.1.3.
4.2 DAMAGE PROGRESSION IN THE WALL SPECIMENS
Minor flexural cracks were visible in all the specimens at the end of the first cycle at a
drift of 0.25%. Damage at drifts of 0.5% consisted of hairline flexural-shear and diagonal
cracks with widths of less than 0.01 in. However, as the applied drift increased,
differences were observed in the behavior of the specimens that led to different failure
modes. The overall behavior of each specimen will be described in the following sections
and photos of the cracking patterns will also be provided. The test results for all the
specimens are also summarized in Table 4-1. As noted in the table, the drift capacity of
the wall is defined as the maximum drift up to which the specimen could sustain at least
80% of the peak load in each loading direction.
4.2.1 Reinforced Concrete Wall Specimens
Specimen S1, with a wall shear span-to-length ratio of 1.2, was constructed with regular
concrete and detailed according to the seismic provisions of Chapter 21 of the ACI Code
(ACI Committee 318, 2005). This specimen sustained a drift of 2.3% with an average
peak shear stress of (psi) ( and (psi)) for the positive and negative
loading direction, respectively). The main crack formation in Specimen S1 had already
occurred by the end of the 0.7% drift cycle and it consisted of three major diagonal
cracks in each direction and some hairline-size flexural cracks. As the test progressed, the
existing diagonal cracks extended and widened and at 1.0% drift, the maximum diagonal
crack width was approximately 0.03 in. Fig. 4-6(a) shows the damage of Specimen S1 at
1.0% drift. At drifts larger than 1.0%, the damage in the wall concentrated at a few major
diagonal cracks and in the cold joint at the wall-foundation interface. Vertical cracking in
the wall compression zone and some concrete spalling at the wall edges was noticeable at
the base of the wall at a drift of 1.7%. In the last loading cycles, damage was
concentrated in the lower part of the wall with diagonal crack widths of up to 0.12 in. On
71
the wall tension side, there was a gap of approximately 0.2 in. at the interface between
the bottom of the wall and the base block due to yielding and slip of the main vertical
reinforcement. At this stage, sliding shear deformations at the wall base clearly governed
the behavior of the specimen and a decision was made to terminate the test, even though
the wall could still sustain 90% of the peak load. Fig. 4-6(b) shows the state of damage
for Specimen S1 at the final drift of 2.3%, while Fig. 4-6(c) presents a close-up of the
damage in the wall boundary region.
Specimen S4 had the same aspect ratio as Specimen S1, but was designed for a higher
shear stress demand. For this specimen the average maximum shear stress demand was
(psi) ( and (psi) for the positive and negative loading direction,
respectively) and the drift capacity was approximately 1.5%. At a drift of 1.0% a more
dense array of cracks had formed compared to Specimen S1, as can been in Fig. 4-7(a).
Appreciable shear-related damage on the lower part of the wall was evident at the end of
the 1.3% drift cycle, with measured diagonal crack widths equal to 0.07 in. At a drift of
1.5%, the wall exhibited significant concrete cover spalling and concrete crushing in the
web region at the lower part of the wall. At this drift the specimen started to loose
strength and the maximum crack width increased to 0.1 in. As the applied displacement
increased, a rapid deterioration of the concrete core in the web of the wall was obvious,
along with a residual opening of the gap at the cold joint, leading to a significant drop in
the lateral load capacity during the drift cycles to 1.5% and 1.9%. The state of damage at
a drift of 1.9% is shown in Fig. 4-7(b). The test was terminated after the wall was pushed
to 2.4% drift and it could sustain only 30% of the peak load. After the removal of the
load, the condition of the concrete core in the wall lower level was examined. Extensive
cover spalling was observed at the wall boundary regions, but no indication of buckling
of the main longitudinal reinforcement was observed. On the other hand, the concrete
core in the wall web was crushed and several vertical bars were fractured. Figure 4-7(c)
shows the extensive damage in the lower part of the wall at the end of the test. Compared
to RC Specimen S1, the damage was more extensive because of the increased shear stress
reversals applied to Specimen S4.
72
Specimen S6, with a shear span-to-wall length ratio of 1.5, sustained a maximum shear
stress equal to (psi). The damage progress in the early cycles was similar to that
in the other reinforced concrete specimens. An array of intersecting diagonal cracks had
already formed in the web of the wall at a drift of 0.5%, along with several hairline-size
flexural-shear cracks that propagated towards the compression zone. The damage at the
drift level of 0.9% can be seen in Fig. 4-8(a) and is similar to that in Specimen S1. A
maximum crack width of 0.02 in. was measured at this drift level. Gradual opening of the
existing cracks rather than the development of new cracks, as well as damage
concentration at the wall compression corner as a result of the initiation of a sliding shear
mechanism, characterized the damage progression up to a drift of 1.4%. In the cycles
leading to a drift of 1.9%, there was deterioration of the concrete in the compression zone
and eventually concrete crushing in the wall compression edges, but no significant loss of
the lateral load capacity was observed. The test was not continued after the drift level of
2.1% because of the substantial damage in the wall boundary elements. Vertical splitting
along the longitudinal reinforcement in the boundary elements was also noticeable. Fig.
4-8(b) shows the state of the damage for Specimen S6 at the end of the test, while a
close-up of the boundary region is shown in Fig. 4-8(c).
Specimen S9 had the same geometry as Specimen S6, but the maximum applied shear
stress was equal to (psi). In the cycles leading to a drift of 0.7%, several flexural
cracks formed and intersecting flexural-shear and diagonal cracks extended towards the
wall compression zone, as can been in Fig. 4-9(a). At this stage, the damage state was
characterized by narrower crack spacing and slightly wider crack widths compared to
Specimen S6. During the cycle at 1.0% drift, the opening of a 0.1 in. wide gap was
noticed on the tension face at the wall base. Specimen S9 maintained its strength up to a
drift of 1.2%. At this drift, the maximum diagonal crack width was equal to 0.08 in. and
0.15 in. for the web and boundary region, respectively. Vertical splitting cracks were also
observed at the wall edges. The wall of Specimen S9 experienced a drop in the lateral
load-carrying capacity during the cycle leading to a drift of 1.5%. Significant concrete
cover spalling and concrete crushing at the lower portion of the wall was evident at a drift
73
of 1.8%. At this drift level, the specimen had lost approximately 25% of its peak load.
Fig. 4-9(b) shows a close look at the wall boundary region after the 1.8% drift cycle was
completed. At the final drift of 2.2%, severe damage concentration at the compression
edge in the lower part of the wall was observed, as can be seen in Fig. 4-9(c).
Examination of the wall after the end of the test revealed several fractured vertical web
bars and a severely damaged wall web.
4.2.2 High-Performance Fiber Reinforced Concrete Wall Specimens
Specimen S2 had the same aspect ratio as Specimen S1, but was constructed with a
hooked steel fiber reinforced cementitious material. The provided horizontal and vertical
web distributed reinforcement was only one-third compared to companion RC Specimen
S1 and the confining reinforcement in the boundary regions was completely eliminated.
Despite the relaxed reinforcement detailing, Specimen S2 sustained a drift of 3.0% with a
maximum shear stress of (psi) and (psi) in the positive and negative
loading direction, respectively. Up to a drift level of 1.2%, minor shear-related damage
was observed in the wall, as can been seen in Fig. 4-10(a). At this stage the maximum
diagonal crack width was approximately 0.02 in., but a gap along the base cold joint
could already be seen. At a drift of 1.5%, no appreciable damage was observed on the
extreme compression fibers at the wall base for both loading directions even though no
confinement reinforcement was used in the wall boundary regions. Several cracks,
however, had formed in the wall boundary regions. As the wall was displaced to a drift of
1.5%, some new vertical splitting cracks formed in the compression zone at the wall base
(Fig. 4-10(b)). At this stage, several cracks of smaller width compared to RC Specimen
S1 were observed, as the fibers were effective in bridging these cracks. In addition,
concrete spalling was minor, even at the boundary regions. As the applied displacement
increased to 2.3% drift, the wall was able to maintain its strength in the negative loading
direction, but experienced some loss of strength in the positive loading direction. At a
drift of 3.0%, it was obvious that the slip at the wall base was excessive and the test was
terminated. Fig. 4-10(c) shows the extent of the damage at the end of the test, while a
close-up shot of the boundary region is shown in Fig. 4-10(d). It should be mentioned
74
that no dowel reinforcement at the wall base was added in this specimen, in an effort to
evaluate whether strengthening the cold joint at the wall base was needed in very short
walls in which shear deformations, rather than flexural yielding, would likely dominate
the wall behavior. However, as it will be discussed in Section 4.6, the results from the test
of Specimen S2 clearly indicated the need for such reinforcement in order to prevent the
opening of a wide through crack at the wall base that can adversely control the wall
behavior.
Specimen S5 was constructed with a self-consolidating HPFRC material with high
strength hooked steel fibers and was designed to resist a higher shear stress demand
(approximately (psi)) compared to Specimen S2. Specimen S5 exhibited a drift
capacity of 1.5%, as companion RC Specimen S4, despite the relaxation in the
confinement reinforcement in the wall boundary regions (one-fourth of the confinement
reinforcing ratio provided in Specimen S4). In terms of damage progression, up to the
drift at which the wall experienced the peak load (0.85%), a significantly larger number
of flexural and diagonal cracks was observed compared to Specimen S4, which can be
attributed to the multiple cracking behavior of the strain-hardening HPFRC matrix (Fig.
4-11(a)). Diagonal crack widths of about 0.02 in. were measured at this stage. At the drift
of 1.3%, the damage started concentrating at the horizontal crack that formed along the
end of the bonded region of the dowel bars, as can be seen in Fig. 4-11(b), and the wall
started to experience a gradual loss of strength. At a drift of 1.7%, the maximum width of
this horizontal crack was 0.1 in. and a noticeable slip was observed along this crack. In
addition, concrete spalling was considered relatively minor compared to that in Specimen
S4 and no vertical splitting at the boundary elements was observed. In the cycle leading
to a 1.9% drift, the pull-out of the fibers bridging the horizontal crack was followed by
significant sliding shear deformations that led to a 30% loss of the specimen strength. At
this stage, concrete spalling was relatively minor and there was no indication of
instability in the boundary regions despite the low confinement reinforcement ratio (Fig.
4-11(c)). The test continued up to a drift of 2.4% and the extensive damage along the
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horizontal crack at the end of the bonded region of the dowels at this drift can been seen
in Fig. 4-11(d).
Specimen S7 had the same geometry as RC Specimen S6, but was reinforced with a 2.0%
volume fraction of hooked steel fibers. This specimen exhibited a diagonal tension failure
at a drift of approximately 2.4%. Diagonal cracks started to form in the wall at 0.25%
drift, along with some flexural cracks. At 0.5% drift, the wall was crossed by several
diagonal cracks and at 1.0% drift, the crack width was 0.02 in. (Fig. 4-12(a)). In the
subsequent drift cycles, the damage in the wall started to concentrate on these cracks,
leading to a crack width of 0.08 in. at 1.5% drift. At 2.0% drift, some minor crushing was
observed on the extreme compression fibers at the wall base, and there was no significant
gap on the tension side at the wall-base block interface. However, flexural-diagonal
cracks were observed near the end line of the dowel bars. Specimen S7 was subjected to a
maximum shear stress of (psi) and sustained about the same drift as the
companion RC Specimen S6 (2.1%), even though the provided reinforcement in the web
and boundary regions of the wall was significantly reduced and placed in one layer. The
state of damage in Specimen S7 at the end of the test is shown in Fig. 12(b).
The damage progression in Specimen S8 with the same geometry and reinforcement as
Specimen S7 but with a 1.5% volume fraction of Spectra fibers, was similar to that in
Specimen S7. At 0.5% drift, the wall was crossed by four main diagonal cracks
corresponding to each loading direction and at 1.0% drift, new diagonal cracks had
formed with approximately 4 in. spacing and a maximum width of 0.03 in. The use of
Spectra fibers resulted in a more dense array of cracks compared to Specimen S7, as can
be observed in Fig. 4-13(a). At 1.5% drift, tens of hairline diagonal cracks had formed
near the major cracks, and the maximum width of the major diagonal cracks was 0.06 in.
On the tension side of the wall, there was a 0.15 in. gap at the interface between the wall
bottom and the base block due to yielding and slip of the main vertical reinforcement. At
displacements larger than 1.5% drift, the damage in the wall was concentrated on a few
major diagonal cracks, and some minor crushing on the extreme compression fiber of the
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wall base was observed. Specimen S8 sustained a maximum shear stress of (psi)
at a drift of 2.1%. Fig. 4-13(b) shows the condition of the specimen at 2.1% drift. At the
final drift of 2.3%, the wall lost more than 20% of its peak strength.
The use of a self-consolidating HPFRC material in Specimen S10, with a shear span-to-
length ratio of 1.5, led to an enhanced behavior compared to that of Specimen S9,
constructed with regular concrete and reduced transverse reinforcement. It should be
reminded that some problems were encountered during the casting of the wall in this
specimen, as discussed in Section 3.3.1.2. Specimen S10 sustained a peak drift of 2.2%
with a maximum applied shear stress of and (psi) for the positive and
negative loading direction, respectively. During the cycles to drifts ranging from 0.15%
to 0.7%, several hairline-size diagonal cracks formed for each loading direction, with the
cracking progressing in the wall web and the extreme compression fiber. The maximum
crack with at 0.7% drift was equal to 0.015 in. No appreciable shear-related damage was
noticeable at a drift of 1.0% and a dense array of narrow flexural and diagonal cracks was
observed in the wall, as in all the HPFRC specimens (Fig. 4-14(a)). At a drift of 1.4%, a
horizontal crack had completely formed in the web of the wall along the end line of the
dowel bars, similar to Specimen S5 (Fig. 4-14(b)). This crack connected with existing
cracks at the boundary elements and in the subsequent loading cycles, damage
concentrated along this crack with visible slip. At a drift of 1.9%, there was minor
concrete spalling with no appreciable damage in the boundary elements (Fig. 4-14(c))
despite the relaxed confinement reinforcement and the high shear stress demands. The
test was terminated at a drift of 2.2% because of damage concentration along the major
horizontal crack. At this drift level, the wall could sustain more than 90% of the peak
load in both loading directions. The state of damage at the lower part of the wall when the
test was terminated is shown in Fig. 4-14(d).
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4.2.3 Summary of Test Observations
The RC low-rise walls designed according to the seismic provisions of the ACI Code
(ACI Committee 318, 2005) exhibited a stable hysteretic behavior with no premature
shear failure. However, a horizontal crack at the wall-foundation interface developed in
the RC walls and the sliding shear deformation mechanism had a significant effect in the
wall behavior at later stages of the test. Damage concentrated in the lower part of the wall
and shear-related diagonal cracking was considered moderate. Specimens S1, S6 and S9
exhibited a similar failure pattern, which was characterized by crushing on the extreme
compression fibers at the wall base and vertical splitting cracks in the wall boundary
regions. In Specimen S4, severe concrete spalling, followed by crushing of the web
concrete, characterized the wall failure at the end of the test. In general, a more dense
array of cracks developed in the RC walls that were tested at a high shear stress level (i.e.
Specimens S4 and S9) compared to the specimens tested under moderate shear stress
reversals (i.e. Specimens S1 and S6).
HPFRC Specimen S2 had a similar failure pattern compared to the companion RC
Specimen S1, but the effect of the sliding shear mechanism at the wall base was
substantially more pronounced. The addition of dowel bars in Specimens S5 and S10
resulted in flexural-diagonal cracks near the end line of the dowels that ultimately led to
failure when the fibers bridging those cracks pulled-out. Specimen S8, reinforced with
Spectra fibers, failed by diagonal tension, whereas loss of strength in Specimen S7 was
due to a combined diagonal tension failure and opening of a horizontal crack along the
end line of the dowel bars. A dense array of narrow cracks developed in the HPFRC
walls. Concrete spalling, if any, was not substantial, even at drifts in the order of 2.0%.
All the HPFRC test units showed a stable hysteretic behavior despite the relaxed
confining reinforcing detailing in the boundary regions. Moreover, the premature sliding
shear failure of Specimen S2 demonstrated the need for dowel reinforcement at the wall-
foundation interface in HPFRC low-rise walls.
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4.3 LATERAL LOAD VERSUS DISLACEMENT RESPONSE
The lateral load versus drift responses for all the test specimens are shown in Figs. 4-
15(a) to (i). The drift in the plots corresponds to the wall lateral displacement with respect
to the wall base and was calculated as described in Section 4.1.2. In each plot, a line
corresponding to the probable shear demand associated to a flexural failure, , is
shown. The probable shear demand was calculated based on the peak moment obtained
from a moment versus curvature nonlinear section analysis using actual material
properties. More information on the nonlinear section analysis is given in Section 5.2.3.
Also shown in the plots is a line that corresponds to the nominal shear strength, . In the
case of the RC walls, the nominal shear strength was calculated based on the 2005 ACI
Code equation (see Section 3.2.2. For the HPFRC walls, the nominal shear strength was
estimated assuming a contribution from the “fiber-reinforced concrete” equal to
(psi), as described in Section 3.2.2. In all cases, measured steel yield strength and
concrete cylinder strength were used for calculation of the nominal shear strength. The
values of the probable shear demand and nominal shear strength are listed in Table 4-2.
From Figs. 4-15(a) to (i), it can be seen that the strength of the test specimens was very
close to the predicted strength. Except for Specimens S7 and S8, which were designed to
exhibit a diagonal tension failure, the predicted strength corresponded to the shear at peak
moment calculated from a moment versus curvature analysis. In these specimens, the
nominal shear strength exceeded the probable shear demand by at least 24% (Specimen
S9) and by as much as 107% (Specimen S1). In Specimens S7 and S8, on the other hand,
the nominal shear strength was slightly lower than the probable shear demand
corresponding to a flexural failure and was very similar to the measured shear strength.
In all the specimens, significant pinching can be seen in the hysteresis loops even for low
drift levels, as expected for low-rise walls, due to major effect of shear at the behavior of
low-rise walls. The well known characteristic in RC elements subjected to cyclic loading
of the unloading and reloading stiffness reduction is also evident in the hysteresis loops.
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The pinching of the loops in the wall specimens constructed with HPFRC materials is
comparable to that of the RC wall specimens. This is attributed to the fact that the fibers
do not provide appreciable resistance against crack closing, despite their effectiveness in
restraining crack opening. It can also be noticed that the load versus drift response for
most of the specimens was not completely symmetrical, mainly due to the correction of
the applied drift to account for the rigid body rotation of the specimens. During the test of
the specimens, the applied lateral displacement was only corrected for the horizontal
displacement of the base block, while the effect of rigid body rotation above
Potentiometer P11 was accounted for only when the results were analyzed. In most cases,
it was found that the rotation of the base block was larger when the actuator was
“pushing” the wall, resulting in somewhat smaller actual applied drifts in this loading
direction (positive direction).
The load versus displacement relationship for RC Specimen S1 is shown in Fig. 4-15(a).
The specimen was loaded uni-axially in the west-east direction, the east direction being
the positive direction in the plot. The first loading half-cycle to a target drift of 0.125%
was in the west direction, corresponding to the actuator “pulling” the specimen. The
specimen exhibited a stable hysteretic response, which indicates that RC low-rise walls
designed according to the seismic provisions of the ACI Code (ACI Committee 318,
2005) can perform adequately under moderate shear demands. Yielding of the main
longitudinal bars was first detected at a drift of 0.75% in the negative loading direction
and by 1.2% drift, yielding had spread along the main longitudinal bars over half the
height of the wall on both sides. At this drift level, sliding deformations at the base of the
wall became significant for the negative loading direction, resulting in a slightly lower
wall shear resistance of the specimen for this loading direction. However, the wall was
able to sustain the peak load up to a drift of 2.3% and 2.5% in the positive and negative
loading direction, respectively. This drift cycle was the last to be applied Specimen S1.
At the end of the test, slip at the wall-foundation interface accounted for approximately
50% of the applied displacement and as a result, the flexural and shear deformation
demands imposed on the wall were relatively small.
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The hysteretic response of HPFRC Specimen S2 is shown in Fig. 4-15(b). The sign
convention in the plot is the same as that used for Specimen S1, i.e. positive displacement
corresponded to “pushing” the specimen. Specimen S2 had the same amount of boundary
longitudinal reinforcement as the companion RC Specimen S1, but the web vertical and
horizontal reinforcement was less than one-half of that provided in Specimen S1. In
addition, no confinement reinforcement was used in the wall boundary regions, relying
solely in the fibers to delay crushing of the concrete and buckling of the longitudinal bars.
In the early cycles the hysteretic response of Specimen S2 was similar to that of
Specimen S1, but a reduced stiffness was recorded for the positive loading direction for
no apparent reason after 0.5% drift. The main longitudinal reinforcement started yielding
at a drift of 0.7% and 0.9% for the negative and positive loading direction, respectively.
At this drift level, strains above yield were recorded up to the mid-height of the wall. In
the cycle after the onset of yielding of the main vertical reinforcement, the peak shear
stress was reached, with a smaller value in the positive loading direction compared to the
negative loading direction. Sliding shear deformations at the cold joint were clearly
significant at this point. The slip along the horizontal crack at the wall base for the
positive loading direction was approximately 8 times that for the negative loading
direction, which resulted in a reduced strength and stiffness for the positive loading
direction. Specimen S2 sustained the full peak stress in the negative loading direction (up
to approximately 3.0% drift) and more than 80% of the peak stress in the positive loading
direction at a drift of 2.3%. After the cycle to 2.3% drift was completed, the drift was
unintentionally increased to approximately 3.0% in the positive loading direction. At this
drift level no loss of strength was observed, but the test was terminated because excessive
base sliding shear deformations had occurred and the wall was “rocking” about its lower
corners, with minor flexural and shear deformation demands above the wall base.
Figs. 4-15(c) and (d) show the lateral load versus drift response for Specimens S4 and S5,
respectively. Specimen S4 was constructed with regular concrete, whereas a self-
consolidating HPFRC material was used in Specimen S5, allowing for some relaxation in
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the required reinforcement. Dowel bars were also used to strengthen the wall-foundation
interface, based on the test results of Specimen S2. The initial cracked stiffness for both
specimens was greater compared to that of Specimens S1 and S2 because of the increased
longitudinal reinforcement ratio. Yielding in the main longitudinal bars in the boundary
region was first detected at a drift of approximately 0.4%, and strains above yield were
recorded in the main vertical reinforcement over half the height of the wall. In Specimen
S5, the strains in the dowel reinforcement were below the yield strain. RC Specimen S4
wall sustained a peak load 20% greater than that of the HPFRC low-rise wall because of
the greater flexural capacity of Specimen S4. As can be seen in the plots, HPFRC
Specimen S5 exhibited a gradual loss of strength and stiffness for drifts larger than 1.0%
and maintained at least 80% of the peak strength up to approximately 1.5% drift. On the
other hand, strength degradation was faster in RC Specimen S4 due to the extensive
concrete crushing in the lower part of the wall. However, Specimen S4 could be
considered to have approximately the same drift capacity as Specimen S4.
Fig. 4-15(e) shows the hysteretic response for RC Specimen S6, with a wall shear span-
to-length ratio of 1.5. The load versus drift response was very similar to that of the
shorter RC Specimen S1. The wall sustained the peak stress of (psi) up to a drift
of 2.1%, despite the damage in the extreme compression fibers at the wall base. A stable
hysteretic response was also exhibited by Specimens S7 and S8, as shown in Figs. 4-15(f)
and (g), respectively. The shear stress that was sustained by these specimens was
approximately equal to that of the control RC Specimen S6. Specimens S7 and S8 did not
experience any significant loss of strength up to 2.1% drift. The type of the fibers used
(hooked steel fibers versus Spectra fibers) did not seem to affect the deformation capacity
of the specimens and the ultimate drift for both specimens was 2.1% and 2.3% for
Specimens S7 and S8, respectively.
The hysteretic response for Specimens S9 and S10, the two specimens with a shear span-
to-wall length ratio of 1.5 that were tested under high shear stress reversals, is given in
Figs. 4-15(h) and (i), respectively. Specimen S9 was constructed with regular reinforced
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concrete, whereas hooked steel fibers were used in Specimen S10, which had reduced
web distributed and confining reinforcement ratios compared to those in RC Specimen
S4. The load versus displacement response was quite similar in the two test walls for
drifts up to 1.5%. In the cycle leading to a drift of 1.75%, a substantial loss of strength
was observed for Specimen S9 due to concrete crushing in the lower part of the wall. The
HPFRC specimen, on the other hand, sustained most of the peak load with a rather
gradual loss of stiffness up to a drift of 2.2%. Fig. 4-16 shows a comparison plot for the
shear stress (normalized by in psi units) versus the drift response for these two
specimens. The peak shear stress level sustained by the HPFRC specimen was slightly
lower than that for the RC wall due to differences in longitudinal reinforcement detailing.
The stable hysteretic response and enhanced deformation capacity of Specimen S10
under such high level of shear stress and despite the reduced reinforcement detailing is a
clear indication of the ability of the HPFRC material to contribute to wall shear strength
and deformation capacity.
4.4 LOAD VERSUS DRIFT ENVELOPE RESPONSE
The load versus drift envelope response for all specimens is plotted in Figs. 4-17(a) to (i).
In the figures, every point in the envelope represents the maximum drift and
corresponding load in each cycle. The first and second cycles to each drift level are
plotted separately with a solid and dashed line, respectively. The values of maximum
drift and load in each cycle for all the specimens are listed in Tables 4-3 to 4-11.
Specimens S4, S5, S9 and S10, designed for a higher shear stress level, seemed to have a
higher stiffness compared to the rest of the specimens, especially in the earlier cycles.
Even though an increased initial stiffness was expected due to the higher reinforcement
ratio, this observation should be taken with some precaution because of the difference in
the calculation of wall drift, as discussed earlier (see Section 4.1.2). The applied
displacement in Specimens S1, S2, S6, S7 and S8 was not corrected to account for
potential slip in the load application mechanism and as a result, the response of these
specimens was slightly “softer”, especially in the earlier drift cycles.
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Within the elastic range, the load versus drift envelope response for the second cycle at
each drift was very similar to that for the first cycle. A small decrease in strength was
observed in some test units after the peak load.
4.5 AVERAGE SHEAR STRAINS
As it was discussed in Section 4.1.3, the average wall shear strain was calculated using
two diagonal potentiometers (see Figs. 3-28 and 3-29) over a wall area of
The lateral load versus average shear distortion response for all test units except fir
Specimen S1 is shown in Figs. 4-18(a) to (h). During the test of Specimen S1 the two
diagonal potentiometers performed poorly and no meaningful calculation could be made
for the average shear strain. As was discussed earlier, the RC walls generally experienced
concrete spalling for drifts larger than 1.5%. As a result, the readings from the
potentiometers were affected and the data presented had to be cut off when they were
considered unreliable. This was not the case for the HPFRC specimens.
For specimens where the Optotrak markers were also used, the average shear strain
calculated from Eq. (4-4) could also be obtained using the data from the corner markers
over a wall area of (see Fig. 3-30). A comparison of shear strains
obtained through the two instrumentation schemes is presented in Fig. 4-19 for Specimen
S5. The two instrumentation schemes generally gave similar results, but the
potentiometers slightly underestimated the shear distortion of the wall.
The load versus average shear strain hysteresis loops for all the RC and HPFRC walls
except for Specimen S2 (and Specimen S1 for which data were not reliable) exhibited
significant pinching. As it was discussed earlier, pinched hysteresis loops are expected
for the HPFRC specimens since the fibers that bridge the cracks cannot offer appreciable
resistance during crack closing, leading to a lower stiffness until the cracks are fully
closed, as is the case for RC members.
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Generally, the shear distortion capacity of the RC specimens was not significantly
affected by either the wall aspect ratio or the level of the applied shear stress. The RC
walls exhibited smaller shear strains compared with the HPFRC specimens, especially for
drifts after peak load. Figs. 4-18(b) and (g) show the load versus shear strain hysteresis
loops for Specimens S4 and S9, respectively. The data were clipped off at about 1.9%
and 1.2% drift for Specimens S4 and S9, respectively, and the two walls exhibited similar
behavior up to shear strains of approximately 0.005 rad (up to 1.0% drift). As it can be
seen in Fig. 4-18(b), Specimen S4 sustained a shear distortion of 0.007 rad and 0.014 rad
in the positive and negative loading direction, respectively, before a significant drop in
strength occurred at 1.9% drift. At this stage, the shear related damage could be described
as moderate. Shear strains were slightly smaller in Specimen S9, with values of about
0.005 rad at 1.2% drift. As can been seen in Fig. 4-9(c), the damage in Specimen S9 was
concentrated at the bottom corners of the wall, resulting in smaller shear distortions. Fig.
4-18(d) presents the load versus average shear distortion response for Specimen S6 up to
a drift of 1.6%. The maximum shear strain measured up to that stage was approximately
0.007 rad and the overall behavior was similar to that in the other RC walls. Based on the
above results, and even though shear strains could not be accurately measured up to
failure of the RC specimens, it can be concluded that moderate shear related damage in
RC walls is associated with shear strains varying between approximately 0.005 rad and
0.007 rad .
The load versus shear distortion response for the wall of Specimen S2 is shown in Fig. 4-
18(a). Specimen S2, reinforced with hooked steel fibers, exhibited minor shear-related
damage with a maximum shear strain of 0.002 rad (negative loading direction). It is clear
that shear deformations had a negligible role in the behavior of Specimen S2, which was
governed by the sliding shear mechanism as well as rocking at the base of the wall, as
explained earlier. It is worth mentioning that the shear strains were even smaller in the
positive loading direction, for which the recorded slip at the cold joint was greater and
less diagonal cracking was observed.
85
Shear distortions in all the other HPFRC specimens (Specimens S5, S7, S8 and S10) were
larger when compared to their companion RC specimens. Shear strains in excess of 0.02
rad were recorded in these specimens and only minor shear related damage was evident
in the walls at distortions of about 0.01 rad. Damage localization started at shear strains
larger than 0.015 rad, which can be conservatively considered as the shear distortion
capacity of the HPFRC specimens.
Figs. 4-20(a) and (b) show the shear distortion versus drift envelope curves for the half-
cycle direction that corresponded to the larger shear strain values (positive or negative
loading direction) for the RC and HPFRC specimens, respectively. From the figures, it is
clear that the rate of shear strain increase was larger for the HPFRC specimens compared
to the RC specimens. It can also be seen that the shear strains for Specimen S2 were
insignificant and basically had no effect on the behavior of the wall specimen. For drifts
lower than 1.0% (limited yielding had occurred at this drift level) the shear distortion was
approximately 0.005 rad for all the HPFRC specimens, except for Specimen S2. For
drifts larger than 1.0%, on the other hand, the shear strains increased at slightly different
rates in the HPFRC walls and at a drift of 2.0%, the maximum shear strain ranged
between 0.018 and 0.024 rad, with Specimen S5 sustaining the largest shear distortion.
A comparison of the shear distortion calculated using Eq. (4-4) and by averaging the
shear strain calculated over the different longitudinal strips along the wall is presented in
Fig. 4-21 for Specimen S4. For drifts up to 1.0% there is good agreement between the
two methods. For the cycles leading to a drift of 2.0%, however, shear distortions
calculated using Eq. (4-4) overestimated the shear distortion with an error in the range of
10% to 20%. For drifts larger than 2.0%, the difference in the results from the two
methods seemed to increase, but the error estimate is not considered accurate because the
recorded data could be unreliable due to concrete spalling. It is worth mentioning that
Massone and Wallace (2004), based on slender RC wall tests, reported that the
calculation of shear distortions using the diagonal transducers mounted within the
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yielding region of the wall tends to overestimate the shear distortion by as much as 30%.
This conclusion generally agrees with the results from this study.
Fig. 4-22(a) shows the shear strain versus drift envelope response for the different strips
(see Fig. 4-4) in Specimen S4 (only the positive loading direction is shown) calculated
from the Optotrak markers data. A similar response was obtained for the RC Specimen
S9. For drifts up to 0.75%, the shear strain was similar for all the strips. However, as the
applied displacement increased, the lower part of the wall (strip 1) exhibited increased
shear strains. Shear strains of up to 0.01 rad were measured in wall strips 2 through 5,
whereas for drifts larger than 1.0% the shear strain in the lower strip increased rapidly
with drift, reaching strains in excess of 0.06 rad. This is explained by the concentration of
shear-related damage on the lower part of the wall after the peak load was reached.
In contrast, increased shear strain values were recorded over a larger area of the wall for
the HPFRC Specimens S5 and S10. The shear strain versus drift envelope for the positive
loading direction in Specimen S10 can be seen in Fig. 4-22(b). Wall strips 1 and 2
exhibited a similar increase in the shear strain after a drift of 0.75%, with strains of about
0.06 rad at the end of the test. It is worth mentioning that Specimens S5 and S10 were
reinforced with dowel bars at the wall-foundation interface and a major horizontal crack
formed in the region where the bonded area of the dowel bars terminated. Horizontal slip
occurred along this crack, which affected the measured values of shear strain for strips 1
and 2, especially during the last drift cycles.
4.6 SLIDING SHEAR RESPONSE
The horizontal slip at the wall-foundation interface was monitored with the use of
potentiometer P12 (see Figs. 3-28 and 3-29), as discussed previously. Fig. 4-23(a) shows
the load versus the base horizontal slip response for Specimen S1. The overall sliding
shear response was not symmetrical for the two loading directions and after the cycle to a
drift of 0.5%, residual slip started accumulating in the negative loading direction. As a
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result, the shear and flexural deformation demand imposed on the wall was greater in the
positive loading direction and yielding of the longitudinal bars at the boundary zone
initiated at a drift of 0.7% for the positive loading direction compared to 1.2% drift in the
negative loading direction. The slip kept increasing in the negative loading direction,
reaching a maximum value of 0.55 in. during the last drift cycle. The load versus slip
hysteresis loops exhibited the well-known pinching resulting in low energy dissipation
capacity for this deformation mechanism.
Significant slip was also recorded in RC Specimen S6, as can be seen in Fig. 4-23(b). For
drifts up to 0.75% the slip was not substantial, with values of less than 0.05 in. After the
onset of yielding of the longitudinal bars in the boundary regions, the wall exhibited
increased sliding shear deformations, especially in the positive loading direction. The
contribution of slip to the overall deformation of the wall in the negative loading
direction was fairly constant throughout the test, but the wall experienced a larger rate of
slip increase in the positive loading direction. In the last drift cycle a slip of 0.5 in. was
recorded, as in Specimen S1.
RC Specimens S4 and S9, which were designed to sustain an increase shear stress
demand, experienced less slip at the cold joint compared with Specimens S1 and S6. The
load versus slip response for Specimens S4 and S9 can been seen in Figs. 4-23(c) and (d),
respectively. The maximum slip was approximately 0.25 in. in both specimens before a
significant drop in load occurred. The observed decrease in slip compared to that in
Specimens S1 and S6 can be attributed to the increased dowel action of the vertical
reinforcement, which led to increased contributions from flexural and shear deformations
to the total drift. In addition, a comparison of the load versus slip response of the RC
specimens did not reveal any influence of wall aspect ratio on the sliding shear
deformations at the base of the walls.
88
For Specimen S2 the potentiometer that was used to monitor the slip at the cold joint did
not work properly for most of the test and reliable results could only be obtained after the
second cycle to a drift of 1.75%. The measured load versus slip response from that point
is shown in Fig. 4-24. As can be seen, the recorded slip at peak displacement for each
cycle was almost constant and, as discussed earlier, the wall experienced larger slip in the
positive loading direction. The sliding shear mechanism in Specimen S2 was initiated
early in the test due to the lack of fibers crossing the wall-foundation interface (and its
effect on concentration of inelastic flexural deformation at the cold joint) and the
insufficient dowel action of the vertical reinforcement at the cold joint. Despite the low
aspect ratio of the wall, the concentrated flexural deformations at the wall base were large
enough to result into a sliding shear failure for this specimen.
All the other HPFRC walls (Specimens S5, S7, S8 and S10) were reinforced with dowel
bars at the cold joint. The addition of the dowel bars forced flexural yielding to primarily
occur above the base of the wall and the measured slip at the wall base did not exceed 0.2
in. for all the HPFRC specimens with dowel bars. However, sliding shear deformations
occurred at the section where the bonded portion of the dowel reinforcement ended and a
predominant horizontal crack developed. For Specimens S5 and S10 it was possible to
obtain data on slip along the horizontal crack using the data from the Optotrak system
markers (see Fig. 3-30). The hysteresis loops are presented in Figs. 4-25(a) and (b) for
Specimen S5 and S10, respectively. In both specimens the measured slip was below 0.15
in. up to the peak load. In the following cycles, the slip increased at a faster rate, with a
noticeable decrease in the slip stiffness and significant pinching. However, the slip
behavior was relatively stable with maximum values of slip of approximately 0.5 in. at
the end of the test. The effect of the slip along the horizontal crack at the end line of the
dowel bars was less significant in Specimens S7 and S8, which failed predominately by
diagonal tension.
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4.7 HORIZONTAL WALL DILATIONS
Wall dilations were measured through potentiometers P3 and P4 (see Fig. 3-28 and 3-29).
In the lower part of the wall, the potentiometers were placed at 4 in. from the wall base,
whereas in the top part of the wall they were positioned at 31 in. from the base. As a
result, for specimens with a shear aspect ratio of 1.2, dilations were obtained at a height
of 0.1h and 0.8h, whereas for the walls with a shear span-to-length ratio of 1.5, dilations
were measured at a height of 0.1h and 0.6h, where h refers to the wall height excluding
the top block.
Figs. 4-26(a) to (c) show the measured dilations at a height of 0.1h and 0.6h for
Specimens S6, S7 and S8, respectively. The dilations at a height of 0.6h in RC Specimen
S6 were 3 to 4 times greater than those at the base of the wall, but were below 0.1 in.
throughout the test (average strain of 0.37%). The same trend was recorded in HPFRC
Specimen S8, but the dilations were larger, with maximum values of 0.1 in. (average
strain of 0.37%) and 0.3 in. (average strain of 1.1%) at the bottom and top of the wall,
respectively. In contrast, dilations in HPFRC Specimen S7 at a height of 0.1h and 0.6h
were similar up to drifts of 2%, with values of up to 0.2 in. (average strain of 0.74%).
Beyond 2% drift, the dilations at the wall base became unsymmetrical and greater than
0.6 in. (average strain of 2.2%).
A comparison of the dilations at the base of the wall for Specimens S9 and S10 is
presented in Fig. 4-27. Greater dilation values were obtained for HPFRC Specimen S10,
which correlates well with the spread of the damage in the lower part of the wall because
of sliding along the horizontal crack at the end of the bonded portion of the dowel bars.
Generally, no significant trend could be obtained with regards to the dilations for the RC
and HPFRC specimens. However, the measured dilations seemed to correlate well with
the damage in the specimens.
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4.8 ROTATIONS
4.8.1 Concentrated Rotations at the Wall Base
As described in Section 4.1.4, the concentrated flexural deformations at the wall base
(over 2 in.) were calculated using the recorded data from potentiometers P7 through P10
(see Figs. 3-28 and 3-29). During the drift cycles leading to failure, there was concrete
spalling and crushing and thus, data recorded from the potentiometers became unreliable
for some specimens. The data were therefore cut off at the point beyond which the
potentiometer measurements were believed to be unreliable. Figs. 4-28(a) to (i) show the
lateral load versus concentrated rotation at the base of the wall for all the specimens. The
concentrated rotation at the wall base was strongly related to the crack opening on the
tension face at the bottom of the wall. As a result, the load versus rotation hysteretic
response became distinctly pinched after the vertical wall reinforcement yielded at the
wall base.
In Fig. 4-28(a) the lateral load versus concentrated rotation response for Specimen S1
was clipped in the second 1.0% drift half-cycle in the positive loading direction, while the
entire data for Specimen S2 are presented in Fig. 4-28(b). Concentrated rotations were
small (below 0.002 rad) in both specimens at the onset of yielding of the wall main
vertical reinforcement. For the RC specimen the concentrated rotation remained small
(approximately 0.003 rad) up to the drift of 1.0%, when the potentiometers stopped
functioning properly. In Specimen S2, for drifts larger than 1.0%, the concentrated
rotations increased at a faster rate for the negative loading direction compared with the
positive loading direction. The maximum value for the concentrated rotation for the
negative loading direction was approximately 0.01 rad, whereas the maximum rotation
demand at the wall base in the positive loading direction was 5 times smaller because of
the substantial contribution of slip to the total drift in this loading direction.
The response of RC Specimen S4 in terms of concentrated rotations is shown in Fig. 4-
28(c), while for HPFRC Specimen S5 the data were cut off at the end of the cycle to
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1.4% drift (Fig. 4-28(d)). The response of both specimens remained linear up to the onset
of yielding of the longitudinal reinforcement at a drift of 0.4%. At this stage the measured
concentrated rotation was, on average, approximately 0.001 rad. Up to a drift of 1.0%,
both specimens exhibited similar response with rotations smaller than 0.004 rad. For
larger drifts, the rotation remained relatively constant for the HPFRC specimen
(Specimen S5) with a value of 0.005 rad up to the time the potentiometers started
performing poorly. In contrast, after the cycle to 1.0% drift, the rotations in Specimen S4
increased faster compared to the previous cycles, with a maximum concentrated rotation
at failure of approximately 0.01 rad.
The behavior of Specimen S6 is shown in Fig. 4-28(e) up to a drift of 1.4%. Small
concentrated rotations (less than 0.002 rad) were measured at a drift of 0.6% when
yielding of the longitudinal reinforcement started. Specimen S6 exhibited higher rotations
compared to Specimen S1 up to a drift of 1.0% (between 0.0025 rad and 0.004 rad). At a
drift of 1.4%, a rotation of 0.007 rad was measured in the negative loading direction,
whereas the wall exhibited a substantially smaller rotation in the positive loading
direction (approximately 0.002 rad). As can been seen in Figs. 4-28(f) and (g), Specimens
S7 and S8 exhibited similar behavior up to a drift of 1.3%, at which the data were cut off
for Specimen S8. At this stage, the peal rotation for Specimens S8 was 0.013 rad. The
rotation at peak load was approximately 0.004 rad for Specimen S7, and a value of 0.007
rad was measured at the end of the test.
RC Specimen S9 exhibited slightly larger rotations compared to the shorter RC Specimen
S4. The load versus concentrated rotation response for this specimen is shown in Fig. 4-
28(h) only up to a drift of 1.0%. At this level the average rotation was 0.006 rad and 0.01
rad for the positive and negative loading directions, respectively. The response for
HPFRC Specimen S10 is presented in Fig. 4-28(i). This specimen exhibited similar
behavior compared with that of RC Specimen S9 up to a drift of 1.0% and by the end of
the test (drift 2.2%), the wall had sustained a concentrated rotation of 0.006 rad.
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4.8.2 Distribution of Rotations along the Wall Height
The maximum total rotations at three sections over the wall height (excluding the top
block), , measured during the first cycle at each drift level, are shown in Figs. 4-29(a) to
(i). The average value of the rotation for the two loading directions is plotted in the
figures. In Specimen S1, the maximum wall rotations at the height of were about
two times those at the height of and the rotations kept increasing with the increase
of drift level. In Specimen S2 most of the rotation experienced by the wall was
concentrated at the height of , whereas the rotation at the height of 0.5 was smaller
compared with Specimen S1. This correlated well with the predominant sliding shear
deformations observed at the bottom of the wall in Specimen S2.
A similar trend was observed in the rotations of Specimens S4 and S5, but the HPFRC
specimen (Specimen S5) exhibited larger rotations at a height of and due to the
horizontal crack that developed in the section where the bonded region of the dowel bars
terminated. The rotations kept increasing with an increase in drift for both specimens up
to a drift of 1.3%. At this point the shear deformations became more significant and
maximum rotations started decreasing.
The rotations in RC Specimen S6 were similar to those in Specimen S1. Up to a drift of
about 1.3% the rotations at a height of were almost two times those at the height of
. For larger drifts, though, the rotations at a height of 0.1 increased at a faster rate
and a maximum value of 0.005 rad was recorded at the end of the test. HPFRC Specimen
S8 exhibited a similar tendency as RC Specimen S6. For HPFRC Specimen S7, however,
the maximum rotations at a height of 0.6h and 0.9h started decreasing beyond 1.8% drift.
This phenomenon correlates well with the fact that the dilations at the wall base of
Specimen S7 were significant after 2.0% drift, which resulted in damage concentration at
the lower part of the wall. After the drift cycle at 1.8% drift, the rotations at 0.1h in
Specimen S7 could not be accurately measured and therefore, were not included in the
plot.
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RC Specimen S9 had a very similar behavior compared with RC Specimen S4, but
Specimen S9 exhibited slightly larger rotations. At a height of , the rotations were
more significant when compared with the rotations at a height of 0 , and
. For drifts larger than 1.3%, the rotations remained fairly constant since shear
distortions started contributing more significantly to the overall drift. In HPFRC
Specimen S10, the rotations at the lower part of the wall (0.1 ) were constant for drifts
ranging from 1.0% to 2.0%, whereas the rotations at a height of increased at a
nearly constant rate with an increase in drift and were up to 3 times larger than the
rotations at a height of . Substantial rotations were also observed at a height of
, but these rotation decreased for drifts beyond 1.8%. At this drift level the rotations
in the lower part of the wall started to increase rapidly due to damage concentration at the
horizontal crack along the end line of the dowel bars.
4.9 STEEL STRAINS
Strains in the reinforcing steel were measured through linear strain gauges. The strain
gauges were attached at several locations on the main vertical reinforcement, the web
vertical and horizontal reinforcement, and the dowel bars. The location and label for the
strain gauges in each specimen is shown in Appendix A (Figs. A-1 to A-8). Before
discussing the strains recorded in the test units it should be mentioned that strain
measurements in reinforcing bars embedded in fiber reinforced concrete tend to be more
sensitive to crack location than those in bars embedded in regular concrete, which is
attributed to the increased bond strength provided by the fibers (Chao et al., 2009). Thus,
the measured strains should not be taken as the only indicator of the degree of inelastic
activity in the wall specimens. Wall rotations and the distribution of curvature along the
wall height also provide a measurement of the inelastic deformations experienced by the
specimens.
In Specimen S1 strains above yield were first recorded in the main vertical reinforcement
at the wall edge near the base (gauges V1, V2 and V3) during the cycle at 0.95% drift.
Yielding spread to mid-height of the wall (gauges V4, V5 and V6) and all strains gauges
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placed on the vertical main and web reinforcement in the lower part of the wall indicated
yielding of the steel. Strains in the main vertical reinforcement at the wall edges located
at the top of the wall (gauges V8, V9) exhibited strains closed to the theoretical yield
value. For drifts exceeding 1.3%, a residual tensile strain at the end of each cycle was
measured in the vertical reinforcement because the bars experienced less compression
strain demands compared to the tension strain demands due to crack opening and wall
“growth”. At the end of the test, tensile strains in the vertical reinforcement of
approximately 1% and 2% were recorded at the base and mid-height of the wall,
respectively. The strain histories for gauges V1 and V5, located at the bottom and the
mid-height of the wall of Specimen S1, respectively, are presented in Fig. 4-30.
Strains in the horizontal bars remained elastic throughout the test and little difference
could be seen between the strain histories recorded at different locations in the horizontal
bars. The strains did not exceed 0.1% and a characteristic strain response is presented in
Fig. 4-31 for a horizontal bar located at from the wall base (gauge H4). It is worth
mentioning that the theoretical yield strain, as obtained from tensile tests, was 0.33% for
the smooth No. 2 horizontal bars used in Specimen S1.
For the companion HPFRC Specimen S2, a similar strain history response was observed
in the main vertical reinforcement at the base of the wall compared with Specimen S1. As
was discussed earlier, the imposed flexural deformation demands were greater in the
negative loading direction because of the unsymmetrical sliding shear response for this
specimen. As a result, yielding was first detected in the bars that were in tension for the
negative loading direction (gauges V4, V2 and V5) during the cycle to a drift of 0.65%.
On the hand, for the positive loading direction, strains above yield were first recorded
during the cycle to a drift of 1.3%The spread of yielding was limited and at wall mid-
height the maximum strain at the end of the test was approximately 0.3%.. Strains in the
horizontal reinforcement were smaller compared to those in Specimen S1, which was
consistent with the minor shear-related damage observed in the wall.
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In Specimen S4, readings from the strains gauges located at the bottom of the wall
(gauges F1-1 and F1-2) gave indication of yielding at a drift of 0.5%. Yielding of the
main vertical reinforcement extended over at least and at mid-height of the wall, a
strain of 0.3% was recorded at 1.0% drift, just before the strain gauges at this location
stopped giving reliable data. The vertical web reinforcement remained elastic for most of
the test and the theoretical yield strain of 0.3% was exceeded at a drift of 1.7% at gauges
located at from the wall base (gauges V1-1 and V1-2). A representative strain
response for the vertical web bars is shown in Fig. 4-32. The high shear stress demand in
RC Specimen S4 resulted in larger strains in the horizontal web reinforcement compared
to those in Specimen S1. At a drift of 1.0%, strains in the horizontal bars of 0.2% were
recorded at all the instrumented locations. Inelastic strains were measured in the
horizontal bar located at from the base of the wall (gauges H3-1 and H3-3).
Similar observations were made in Specimen S5 with regards to the recorded strain
histories in the main vertical reinforcement. The inelastic activity was limited to
approximately from the base of the wall and the strains were in the range of 0.3% to
0.5% (generally larger than those in Specimen S4). The dowel bars that were added to
reinforce the wall-foundation interface remained elastic, but strains in the range of 0.08%
to 0.16% were measured in these bars. The strains in the web vertical and horizontal
reinforcement were generally similar to those in Specimen S4. Yielding in some
horizontal bars took place for drifts larger than 1.5%. Fig. 4-33 shows the recorded strain
history obtained for a horizontal bar located at for Specimens S4 and S5 (gauges
H4-1 and H5-1, respectively).
There was no significant difference in the strain histories for RC Specimen S6 when
compared with RC Specimen S1. In the lower part of the wall strains in excess of 2.0%
were recorded in the main vertical reinforcement at the boundary regions. Fig. 4-34
presents the strain history for a strain gauge located in the mid-height of the wall (gauge
V19) with a maximum recorded strain of 0.6%. Strains in the web vertical and horizontal
reinforcement were either below or approximately at the theoretical yield strain. A
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representative strain history for horizontal bars located at and from the wall
base can be seen in Fig. 4-35.
Readings from linear strain gauges attached to the vertical reinforcement in Specimens
S7 and S8 revealed that most of the reinforcement yielded during the cycles ranging from
0.8 to 1.3% drift. First yielding of the main vertical reinforcement was observed at 0.8%
drift in Specimen S7, and at 1.0% drift in Specimen S8. The dowel bars did not yield
during the test, as was also observed in Specimen S5, but their maximum strain was as
large as approximately 0.1%. Strains close to the theoretical yield strain in the horizontal
reinforcement were observed during the cycle to 1.5% and 1.0% drift for Specimens S7
and S8, respectively. Inelastic strains were also observed in the horizontal bars of
Specimen S8, which failed by diagonal tension.
Yielding at the lower part of the wall for Specimens S9 and S10 was first observed during
the cycle to 0.5% drift. Inelastic activity spread up to from the wall base for
Specimen S10 and strains exceeding 2.0% were recorded during the last cycles. In
contrast, maximum strains of about 0.3% were measured in Specimen S9 at the wall mid-
height, and the strain histories suggested that no yielding took place in that location in the
main vertical reinforcement. Strains in the web vertical reinforcement were in the range
of 0.1% to 0.3% for both specimens. Larger differences were observed for the web
horizontal reinforcement. Fig. 4-36 shows a comparison of the strain history for a strain
gauge located in a horizontal bar at a height of for Specimens S9 and S10 (gauges
H3-1 and H3-2, respectively).
Figs. 4-37(a) and (b) show the strain versus drift envelop response obtained from strain
gauges placed on the main vertical wall reinforcement and located at 1.0 in. from the wall
base in the RC and HPFRC specimens, respectively. For Specimen S1, the strain
increased almost linearly with an increase in drift up to approximately 1.3% drift,
followed by a faster strain increased for large drifts. For Specimens S4, S6 and S9 when
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the strain reached the yield strain (at a strain of about 0.23%), the strain increased at a
much higher rate with an increase in drift. In addition, the strains at ultimate in these
specimens were 2 to 3 times larger than the strains in Specimen S1. Similar observations
were made for the strains in the HPFRC specimens, where yielding started at drifts
ranging from 0.4% to 1.0%.
From Fig. 4-38 (a), which presents the strain versus drift, envelop response obtained from
strain gauges placed on the main vertical reinforcement at the wall mid-height in the RC
specimens, it can be seen that yielding spread up to that location, particularly in
Specimens S1 and S6. Unlike the strain measured at 1 in. from the wall base, the strain
increase at wall mid-height was much greater in Specimen S1 compared with the rest of
the RC walls for drifts larger than 1.7%. In Specimen S9, the damage was concentrated in
the lower part of the wall and as a result, the strain beyond 0.8% drift remained fairly
constant with an increase in the drift.
The strains for the HPFRC specimens at the wall mid-height are shown in Fig. 4-38(b).
Strains in Specimens S2 and S5 with a shear span-to-length ratio of 1.2 remained
constant at about the yield strain, whereas for Specimen S10 a fast increase in strain with
drift was observed after yielding, with strains at ultimate close to 2.0%. A similar trend
was observed during the early loading cycle for Specimens S7 and S8, but the strain
gauges stopped working at a drift of 1.4% and 1.0%, respectively.
The strains for the dowel reinforcement in the HPFRC test units (Specimens S5, S7, S8
and S10) are presented in Fig. 4-39. As was discussed earlier, the strain gauges located on
the dowel bars at 1.0 in. from the wall base showed no sign of yielding and maximum
strains were in the range of 0.1% to 0.16%. Studies by Chao et al. (2009) have concluded
that reinforcing bars embedded in HPFRC materials exhibit a superior bond resistance
compared to regular concrete matrices because of the confinement that the fiber
reinforcement offers, along with the crack control.
98
Based on the readings of the strain gauges located on the dowel bars in Specimens S5 and
S10 at 1 in. from the wall base and at the section where the bonded region of the dowels
terminated, an estimation of the average bond stress could be made. For Specimen S5 the
peak average bond stress was 580 psi (calculated at a drift of 1.0%), whereas a value of
650 psi was estimated for Specimen S10. Using the readings of the strain gauges at the
base of the dowel bars in Specimens S7 and S8, the average bond stress was estimated to
be approximately 550 psi and 700 psi, respectively. It should be mentioned that a larger
bond stress developed in the dowel bars of Specimen S8, which was reinforced with
Spectra fibers, compared to the specimens reinforced with steel fibers.
Figs. 4-40 to 4-42 show plots of strain versus drift for wall horizontal bars located at a
height of , and , respectively. The measured strains in the horizontal bars
located at for the RC walls were significantly affected by the level of the shear
stress and consequently the shear damage experienced by the walls in the lower part. A
similar trend, but less pronounced, was observed in the HPFRC specimens. The strains
measured in the horizontal reinforcement located at were similar in all the
specimens, except for Specimen S2, where much smaller strains were recorded due to
insignificant shear-related damage.
4.10 STIFFNESS RETENTION CAPACITY
The stiffness of the wall specimens was evaluated in terms of the secant stiffness values
determined from peak-to-peak displacement for each hysteresis loop. As can be observed
from the load versus displacement hysteresis loops, the stiffness decreased with an
increase in the drift and the rate of the stiffness decay decreased as the drift increased.
HPFRC specimens had a lower initial stiffness compared with the companion RC
specimens due to the reduced reinforcement in the wall and the lack of aggregates in the
cement-based mixture for Specimens S2, S7 and S8.
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In order to better evaluate the stiffness retention capacity of the specimens, the peak-to-
peak displacement secant stiffness values were normalized with respect to the secant
stiffness at approximately 0.15% drift for each specimen, in order to take into account
variations in specimen parameters, such as the reinforcing ratio and the lack of coarse
aggregate in some of the HPFRC walls. Table 4-12 presents the value of the secant
stiffness used for the normalization in each specimen and the corresponding average drift
level.
Figs. 4-43 (a) to (d) show the normalized peak-to-peak displacement stiffness versus drift
for the first and second cycle for the test units. Specimen S8 showed a similar trend
compared with that in Specimen S7 and thus, it was omitted from the figures. All the
HPFRC specimens had a higher normalized stiffness compared to the RC companion
specimens at the same drift level and maintained a higher percentage of their initial
stiffness at the end of the test. The stiffness values for the second cycles at each drift level
were very close to the first cycle values. It was also observed that shear stress level had
an adverse effect on the normalized stiffness decay because the specimens tested under
moderate shear stress levels exhibited a more gradual loss of stiffness compared to the
specimens subjected to higher shear stresses. This trend can be seen in Figs. 4-44 and 4-
45, where the normalized stiffness versus drift is plotted separately for the RC and
HPFRC walls, respectively, and the level of shear stress sustained by each specimen is
noted for easy comparison.
It should be noted, however, that yielding of the wall main longitudinal reinforcement
had a substantial effect on the decay of peak-to-peak displacement stiffness with an
increase in drift, but this does not necessarily translated into critical damage in the wall.
As a result, the decay of peak-to-peak stiffness should not be taken as the only indication
for the state of damage in the specimens.
100
The experimental initial stiffness of the walls was also compared to the theoretical elastic
stiffness accounting for the effect of shear deformation. However, the experimental initial
stiffness was found to be more than 80% below the theoretical value. Other studies that
have reported pre-cracking stiffness based on shear wall tests generally revealed a wide
scatter in the stiffness values (Cardenas et al., 1980; Farrar, 1990). The difference in the
experimental and theoretical stiffness values can be attributed to the several factors,
particularly elastic opening and slip along the cold joint, as well as slip in the test set-up.
In this study, the instrumentation was not originally designed to accurately measure the
pre-cracking stiffness and further comparison of the experimental and theoretical stiffness
was not considered appropriate.
4.10 ENERGY DISSIPATION CAPACITY
A desirable characteristic in the behavior of low-rise walls, besides adequate
displacement capacity, is a good energy dissipation capacity. The energy dissipated by
the specimens during each loading cycle was calculated as the area enclosed by the
applied load versus displacement hysteresis loops. Figs. 4-46(a) and (b) show the
dissipated energy versus drift for the wall specimens with a shear span-to-length ratio of
1.2 and 1.5, respectively. In these plots, the drift is the average drift reached for the
positive and negative loading directions at each cycle. The first and second cycle at each
drift are plotted separately with a solid and dashed line, respectively. For drifts smaller
than 0.5%, the energy dissipated was quite small, but for larger drifts a nearly linear
energy increase with respect to an increase in drift level can be observed. In all the
specimens, the energy dissipated during the first cycle was slightly larger compared to
that in the second cycle at the same drift level, mainly because of the small decay in the
strength and stiffness that the specimens experienced during the second cycle. Specimens
S7 and S8, which had the same reinforcing detailing but reinforced with steel and Spectra
fibers, respectively, revealed no significant difference in the amount of energy dissipated,
with only a minor change in the trend during the last cycles due to a difference in the
failure mechanism.
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The dissipated energy was also normalized such that specimens with different load-
carrying capacities could be adequately compared. The dissipated energy was normalized
by the energy dissipated by an equivalent elasto-plastic system. The value of the
normalized energy, therefore, provided information about the degree of pinching in the
load versus displacement hysteresis loops. For the calculation of the area enclosed by the
elasto-plastic system, the peak strength of the elasto-plastic system was set equal to the
strength measured in the specimens for each cycle at a given drift level. The stiffness of
the system was set equal to the peak-to-peak stiffness at the first loading cycle to 0.5%
drift. The value of the stiffness for smaller drifts was not considered reliable since it was
greatly affected by the flexibility in the test set up. Nonetheless, the values of the
normalized dissipated energy were quite sensitive to the chosen stiffness definition of the
elasto-plastic system and more attention should, thus, be given to the general trends
rather than the actual values.
The plots of normalized energy dissipated versus average drift for all specimens are
shown in Figs. 4-47(a) and (b). The wall specimens with a shear span-to-length ratio of
1.2 exhibited an almost constant normalized energy dissipation capacity for drifts ranging
from 0.5% to 1.5%. Specimen S2, which failed by sliding shear at the wall base, had
slightly smaller normalized energy than the companion RC Specimen S1, whereas
HPFRC Specimen S5 exhibited a larger normalized energy than RC Specimen S4. In the
group of specimens with an aspect ratio of 1.5, the normalized energy generally increased
with an increase in drift. HPFRC Specimen S10 had the best energy dissipation capacity
among all the specimens for drifts larger than 1.0%. Overall, the HPFRC walls that were
tested under higher shear stress reversals (Specimens S5 and S10) had a higher value of
dissipated energy than the companion RC specimens (Specimens S4 and S9).
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CHAPTER 5 ANALYTICAL STUDIES
5.1 DEFORMATION COMPONENTS
Several deformation mechanisms contribute to wall drift, the most important ones being:
shear distortion, sliding at the base of the wall, and flexural rotations (elastic and
inelastic). In this section, an attempt was made to determine the relative contributions
from each of these components to total drift.
The deformation components were calculated using the data recorded from either the
potentiometers and clinometers or the Optotrak system. For Specimens S4, S5, S9 and
S10, the Optotrak marker coordinates were used to calculate the deformation components
following the procedure described below. A similar procedure was used for the
specimens where only data from potentiometers and clinometers were available.
The drift due to the shear distortion of the wall was calculated as:
(5-1)
where is the average shear strain in a strip i (where i ranges from 1 through 5 as shown
in Fig. 5-1), is the height of each strip (i.e. 5 in.), and is the wall shear span equal to
48 in. and 60 in. for the wall specimens with a shear span-to-length ratio of 1.2 and 1.5,
respectively. The shear strain in each strip was calculated as described in Section 4.1.3,
based on the coordinates of the Optorak markers.
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The drift due to sliding at the wall base ( was estimated based on the difference
between the horizontal coordinates of the Optotrak markers at the base of the wall (i.e.
first row of markers in the wall) and the foundation block as follows:
(5-2)
where is the average horizontal displacement of the markers at the base of the wall
(in.) with respect to the foundation block, corrected to account for the flexural rotations
within the lower 4 in. of the wall.
The drift due to the flexural rotations within the region instrumented with Optotrak
markers was determined based on the average curvature calculated for each strip by
double integration of the curvature along the wall elevation:
(5-3)
where is the average curvature for strip i calculated as described in Section 5.2.1
(rad/in.), is the distance from the middle of strip i to the mid-depth of the top beam
(in.), and is the height of strip i (in.). These terms are also defined in Fig. 5-2. Elastic
flexural rotations above the wall area instrumented with Optotrak markers were
determined assuming elastic uncracked behavior.
The total calculated drift was then obtained as follows:
(5-4)
Figs. 5-3 (a) through 5-3 (d) show plots of the predicted drift normalized by the applied
drift for Specimens S4, S5, S9 and S10. The average contributions for the two loading
directions are plotted in the figures because similar behavior was obtained for the positive
and negative loading direction. The plots have been separated in three areas. The lower
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region corresponds to the drift due to flexural rotations over the area instrumented with
the Optotrak markers (elastic and inelastic). The contribution of the elastic rotations
above the instrumented region was insignificant (less than 3% in all the specimens) and
thus, it was not added to the plotted contribution from flexural rotations. The middle area
gives the contribution of shear distortions, followed by the upper region, which represents
the contribution of the horizontal slip at the wall base. It can be observed that the
summation of the drift components was in reasonable agreement with the applied drift,
the analytical value ranging between 85% and 110% of the “actual” drift.
The behavior of Specimens S4 and S9 should be representative of that for an RC wall
designed according to the ACI Code Seismic Provisions and subjected to shear stress
reversals of high intensity. The plot of the deformation components for these specimens
is shown in Figs. 5-3 (a) and (b), respectively. Figs. 5-3 (c) and (d), on the other hand,
show the drift components for Specimens S5 and S10, respectively, which refer to the
companion HPFRC walls. It is worth mentioning that the wall of Specimens S5 and S10
was reinforced with dowel bars at the wall-foundation interface and ultimately failed due
to the formation of a wide flexural crack along the end line of the dowel bars, along with
concrete crushing in the lower part of the wall.
Between 50% and 60% of the drift applied to RC Specimen S4 for drifts up to of 1.0%
was contributed by flexural deformations. For larger drifts, however, the contribution of
flexural rotations decreased and the specimen started exhibiting appreciable shear-related
damage in the lower wall region. At the onset of concrete spalling at 1.5% drift, flexural
rotations contributed approximately 35% of the applied lateral displacement. At
approximately 2.0% drift, shear distortion and slip contributed over 70% of the total drift,
the displacement at which the wall experienced a significant loss of strength.
In RC Specimen S9, which experienced substantial concrete crushing in the wall edges
close to the wall base, flexural rotations played a more important role compared to that in
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Specimens S4. The contribution from shear distortions to total drift in this specimen was
relatively constant throughout the test (approximately 20%), while sliding deformations
became significant (greater than 30%) when rotations started decreasing at drifts larger
than 1.3%.
HPFRC Specimens S5 and S10, with a shear span-to-length ratio of 1.2 and 1.5,
respectively, exhibited the same failure mode. The slip contribution at the wall base for
both specimens was less than 10% because of the use of dowel reinforcement. Despite
the similar failure pattern, the increased slenderness of Specimen S10 led to an increase
in the rotation contribution compared to Specimen S5 when the drift exceeded 1.4%.
Conversely, shear distortions contributed more significantly to total drift in Specimen S5
and at a drift of 1.8%, shear distortions contributed more than 50% of the applied drift. It
should be noted, however, that some slip occurred along the horizontal crack that
developed in the region where the bonded part of the dowel reinforcement terminated for
both specimens. This slip translated into an “apparent” shear strain that could not be
separated from the “actual” shear strain. Thus, the shear distortion contributions in
Specimens S5 and S10 also included the contribution of slip along this horizontal crack.
Overall, rotations in Specimens S4, S5, S9 and S10 contributed approximately 60% of the
total lateral displacement for drifts up to 1.0%. For larger deformation levels, however,
the contribution of horizontal slip (either at the cold joint or in the region where the
bonded length of the dowel bars terminated) and shear strains increased, reducing the
wall rotation contribution to total drift.
For Specimens S1, S2, S6, S7 and S8, a similar analysis was performed based on the data
recorded from the potentiometers and clinometers (see Fig. 3-29). In Specimen S1, the
rotations at a height of 0.1h, where h refers to the height of the wall (excluding the top
block), had an almost constant contribution to the total drift throughout the test,
approximately equal to 20% and 10% for the positive and negative loading direction,
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respectively. Rotations between sections located at 0.1h and 0.45h from the wall base, on
the other hand, had an increased contribution to total drift. For the positive loading
direction, a contribution of 25% was calculated for the early cycles, increasing to 40% for
drift levels close to failure. For the negative loading direction, this contribution was
somewhat constant and corresponded approximately to 20% of the total wall drift.
Sliding shear deformations had a significant effect on the behavior of Specimen S1 and
contributed up to 40% of the total drift for the negative loading direction, which explains
the smaller contribution of inelastic rotations at the wall base to total drift.
HPFRC Specimen S2 exhibited a different behavior in terms of drift components
compared to the companion RC Specimen S1. Rotations at 0.1h had an increasing
relative contribution to total drift with an increase in drift demand. For the negative
loading direction, this contribution varied from 30% in the early cycles to 70% in the last
cycles. With respect to the drift contribution in the positive loading direction, flexural
rotations at 0.1h contributed between 10% and 30% of the applied drift. Rotations
between 0.1h and 0.45h had a negligible contribution to total drift (less than 10%). The
small contribution of rotations in this region was due to the predominant sliding shear
mechanism exhibited by the wall. The contribution from sliding deformations was
approximately 60% in the cycles close to failure for the positive loading direction, but
this contribution was only 20% for the negative loading direction, where rotations at 0.1h
played a dominant role. Shear distortions had a negligible contribution, less than 5%, to
total drift. It seems that the relative low shear stress demand on the specimen, combined
with the significant sliding deformations that led to an increased rocking at the wall base,
did not allow for the development of large shear distortions.
Concentrated rotations at the wall base in RC Specimen S6 accounted for approximately
20% of the total drift, whereas inelastic rotations over the rest of the wall height
contributed about 50% of the total drift for both loading directions. Shear deformations
were about six times larger than those in HPFRC Specimen S2, with a contribution of
approximately 20% to total drift. For HPFRC Specimens S7 and S8, wall base rotations
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accounted for less than 50% of the applied lateral displacement, while shear distortions
had an increased contribution (approximately 40% at drifts larger than 1.8%) compared
to the companion RC Specimen S6.
5.2 CURVATURE
5.2.1 Curvature Distribution
Curvature along the wall elevation was computed from the readings of the Optotrak
markers. It was assumed that cross sections remained plane after loading and thus, Eq. (5-
4) was used to compute curvature along the wall height:
(5-5)
where is the average curvature (rad/in.) over each strip i of height (in.), and ,
and and are the y-coordinates of the edge markers at the top and bottom corners
of strip (in.), respectively, and is the horizontal distance between the edge markers,
equal to 35 inches.
The curvature profile along the wall height for Specimens S4, S5, S9 and S10 is plotted
for the first cycle at each drift level in Figs. 5-4 through 5-7. Curvature distribution for
the positive and negative loading directions is plotted separately. In some instances,
particularly near the end of the tests, curvature could not be calculated due to concrete
spalling, which made the deformation measurements unreliable. In each plot, a line
denoting the theoretical yield curvature was added, as obtained from a non-linear section
analysis (see Section 5.2.3). The values for the theoretical yield curvature for Specimens
S4, S5, S9 and S10 are listed in Table 5-1.
For RC Specimen S4, the values of curvature above the lower strip (Fig. 5-2) were below
or at the theoretical yield curvature, , for drifts up to approximately 0.6%. The
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curvature at the bottom strip in the wall, however, was two to four times larger than at
this drift level. For larger drifts, inelastic deformations spread up to 14 in. (0.3h) from the
wall base, whereas the rest of the wall had curvature values below the theoretical yield
curvature.
HPFRC Specimen S5 had a similar curvature distribution compared to that in the
companion RC specimen (Specimen S4) for low drift levels (less than 0.6%). The use of
dowel reinforcement, however, led to increased average curvatures in the strip where the
bonded portion of the dowel bars ended (4 in. to 9 in. from the wall base). Curvatures at
the wall base were also larger for HPFRC Specimen S5 compared to RC Specimen S4. A
behavior similar to that of RC Specimen S4 and HPFRC Specimen S5, respectively, was
observed in Specimens S9 and S10.
5.2.2 Plastic Hinge Length and Curvature Capacity
Several equations exist for the prediction of plastic hinge length in RC beams and
columns, but limited studies have addressed the length of plastic hinges in low-rise shear
walls. Pauley and Priestley (1993) proposed an equation for RC walls that relates the wall
plastic hinge length with its aspect ratio, as follows:
(5-6)
where is the plastic hinge length (in.), i.e. a hypothetical length over which the
maximum curvature is assumed to be constant, is the wall aspect ratio, and is the
wall length (in.). Table 5-2 lists the values of the plastic hinge length for Specimens S4,
S5, S9 and S10 as obtained from Eq. (5-6), as well as those obtained from the test. The
experimental value of the plastic hinge length, , was estimated based on the curvature
distribution obtained from the Optotrak markers (see Section 5.2.1) and corresponded to
the length over which the experimentally obtained maximum curvature could be assumed
constant such that it resulted in approximately the same contribution to wall drift.
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From Table 5-2, it can be observed that specimens with increased slenderness exhibited a
shorter plastic hinge length, as the walls experienced increased concentrated rotations at
the wall base compared with the shorter walls. In the case of the HPFRC walls, the
addition of the dowel bars in the wall-foundation interface led to a wider spreading of
inelastic activity compared to the companion RC specimens. Pauley and Priestley
suggested that Eq. (5-6) is a rather conservative estimation of the plastic hinge length.
However, as it can be observed from the comparison of the values in Table 5-2, the
equation predicted a longer plastic hinge for the RC walls (also for the HPFRC
Specimens) compared with the experimentally estimated plastic hinge length. Thus, for
the case of the specimens in this study Eq. (5-6) would underestimate the curvature
ductility demands.
5.2.3 Section Modeling for Prediction of Moment versus Curvature Response
In order to predict the moment versus curvature response of the critical section in the wall
specimens, a nonlinear section analysis was performed using a computer program
originally written by Parra in the late 1990s (Parra and Naaman, 2001). The program is
based on the common assumption that plane sections remain plane after bending (i.e.
linear strain distribution). This assumption is generally valid for beams that have
relatively long spans compared with their depth, but it could be questionable for deep
members, as in the case of low-rise walls. A linear strain distribution, however, was
assumed for simplicity and the results compared well with the experimental moment
versus curvature response of the walls.
The nonlinear section analysis was performed for Specimens S4, S5, S9 and S10 for
which the analytical results could be compared with the experimental moment versus
curvature response obtained from the Optotrak system. For RC Specimens S4 and S9, the
critical section considered was at the wall base. For the HPFRC specimens, on the other
hand, two sections were analyzed, the section at the wall base and the section where the
bonded region of the dowel bars ended. For the section at the wall base (cold joint), no
tension stresses were allowed in the concrete (for both RC and HPFRC walls).
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For modeling the tensile stress-strain response of the HPFRC material, a piece-wise
linear relationship was used, as shown in Fig. 5-8. The values for the four points were
obtained by fitting the model to the average stress-strain response reported by Liao et al.
(2007). The tensile behavior of regular concrete was assumed linear up to the cracking
point, assumed to occur at a stress of (psi). The values used in the analyses are
summarized in Table 5-3.
The model shown in Fig. 5-9 was used for simulating the compressive behavior of the
regular concrete and the HPFRC material. The ascending portion of the stress-strain
response can be satisfactory modeled as linear up to peak stress (Roy and Sozen, 1964),
followed by a linear stress decay until the compression strain capacity of the material is
reached. This simple model was chosen since the flexural behavior of RC members is not
particularly sensitive to the shape of the matrix compressive stress-strain response. As it
can been seen in Fig. 5-9, the parameters needed to define the compressive stress-strain
response are: the compressive strength , the strain at maximum stress , the slope
parameter for the descending branch, and the ultimate strain .With these parameters
defined, the equations that describe the model are as follows:
For :
(5-7)
For
(5-8)
Table 5-4 summarizes the input parameters that were used for the HPFRC matrix in
Specimens S5 and S10. The values were obtained from cylinders tests conducted as part
of this study, combined with the results reported by Liao et al. (2007) for the same
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HPFRC mixture. For the regular concrete mixture used in Specimens S4 and S9, the
value of the maximum compressive strength was obtained from cylinder tests, whereas
the values of the strain at maximum stress and the slope parameter are shown in Table
5-4.
The behavior of the steel reinforcement was modeled as shown in Fig. 5-10. The required
parameters are the steel yield strength , modulus of elasticity , strain at the beginning
of the strain-hardening region , initial modulus of the strain hardening branch ,
tensile strength , and the strain at tensile strength . The equations that describe the
model are as follows:
For :
(5-9)
For :
(5-10)
For :
(5-11)
For :
(5-12)
where:
(5-13)
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The values for the yield strength and the tensile strength of the steel reinforcement were
obtained from direct tension tests (see Table 3-6). However, the strains in the steel were
not always measured reliably. Thus, the following values were used, which in general
represented well the stress-strain response of the steel for the cases where it could not be
obtained experimentally: , , and .
In order to estimate the curvature capacity of both RC and HPFRC wall sections, a
concrete compression strain capacity needed to be assumed. For the regular concrete
matrix used in RC Specimens S4 and S9, a maximum compressive strain of 0.008 was
assumed because of the good confinement of the concrete core in the wall boundary
regions. The analysis was also performed for a maximum strain values in the range from
0.005 to 0.008, but the results showed that these values are too low to get a reasonable
prediction of curvature capacity. An increased strain capacity was used for the HPFRC
material in the section analysis for Specimens S5 and S10. Parra et al. (2005) reported a
crushing strain of approximately 0.01 in HPFRC (mortar mixture) beams subjected to
displacement reversals. As a result, this limit was used as a first approximation, and
resulted in reasonable predictions of the curvature capacity for the section at the end line
of the dowel bars.
Figs. 5-11 to Fig. 5-14 show moment-curvature plots for Specimens S4, S5, S9 and S10,
respectively. In each plot, the moment-curvature response obtained from the nonlinear
analysis (at the critical section) was compared with the behavior obtained from the
experiments. It can be observed that prior to yielding, the analytical response did not
agree well with the experimental moment-curvature response that corresponded to the
applied moment at the wall base and the average curvature obtained over the lower 4 in.
of the wall. The experimental response was substantially softer compared with the
analytical response, which is attributed to strain accumulation (and potentially slip) of the
wall vertical reinforcement in the base block. However, the curvatures that were
experimentally measured in the wall region from 4 in. up to 9 in. from the wall base were
in very good agreement with the analysis results for curvatures within the elastic range.
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Compared with the experimental data, the results from the theoretical analysis showed
higher moment capacities. As mention earlier, a basic assumption in the analysis was a
linear strain distribution in the wall sections. As a result, the analysis did not consider any
shear-moment interaction, which could be significant in low-rise walls. For Specimen S5
in particular, it seems that the weak region in the section where the bonded part of the
dowel bars terminated affected significantly the wall strength and resulted in a lower
moment capacity compared with that predicted through the nonlinear analysis (Fig. 5-12).
In RC Specimens S9 that failed by concrete crushing at the wall corners near the base, the
curvature capacity (average value for the positive and negative loading directions) at the
wall base was equal to (rad/in.). This curvature capacity is approximately 13
times larger than the theoretical yield curvature for Specimen S9, as obtained from the
nonlinear section analysis. In comparison, RC Specimen S4, which exhibited a web
compression failure and whose behavior was characterized by a reduced contribution
from flexural rotations to total drift, exhibited a curvature capacity equal to
(rad/in.) or about 7.5 times the theoretical yield curvature.
Table 5-5 lists the values of the compressive strains , , and , measured at the edge
of the wall in the regions from 0 in. to 4 in., 4 in. to 9 in., and 9 in. to 14 in. from the wall
base, respectively, for various drift levels. The strains were first calculated using the outer
Optotrak markers and then the strain at the wall edges was estimated based on the
average curvature calculated for that drift level. In Specimen S4, strain , in the regions
where web concrete crushing was concentrated, was estimated to be 0.0012 at 1.0% drift
and increased to 0.0026 at 2.0% drift. For Specimen S9, the compressive strain at a
drift of 1.5% was approximately 0.004, and increased to 0.0085 near the end of the test
(2.0% drift).
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5.3 SHEAR FRICTION MODEL
Several studies have revealed a relation between the shear strength of deep beams and the
amount of horizontal reinforcement (for example, dePavia et al., 1965; Smith and
Vantsiotis, 1982). Based on these observations, Wood (1990) suggested that the shear
strength of RC low-rise walls could be related to the total amount of vertical
reinforcement (longitudinal reinforcement in the boundary elements and wall web
vertical reinforcement), as also discussed in Section 2.2.4.2. Using a shear friction
analogy and assuming a sliding mechanism to develop along the critical horizontal crack,
the nominal shear strength of the low-rise test walls could be estimated as:
(5-14)
where is the shear friction coefficient, is the area of steel crossing the shear plane
(in.2), is the yield stress of the vertical steel (ksi), and is the area of the shear plane
(in.2
). In case that bars with different yield strengths are used in the boundary elements
and the wall web, the quantity can be determined as:
(5-15)
where is the steel area in one boundary region (in.2), is the yield stress of the
steel in the boundary region (ksi), is the area of web vertical reinforcement (in.2
),
and is the yield stress of the web vertical reinforcement (ksi).
The value of the friction coefficient is generally not known and a reasonable lower bound
for low-rise walls equal to was proposed by Wood (1990). Fig. 5-15 shows a plot of
the ratio versus the shear friction strength corresponding to . The
ordinate values correspond to the experimental shear friction coefficient, . The vertical
reinforcement considered was the total reinforcement crossing the critical horizontal
crack that developed in each wall. In the case of the RC walls and the HPFRC specimen
with no dowel bars (Specimen S2), the section considered was at the wall base. On the
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other hand, for the HPFRC walls with dowel bars (Specimens S5, S7, S8, and S10), the
section considered corresponds to the horizontal crack that formed along either the end
line of the dowel reinforcement or at the section where the bonded part of the dowel bars
ended. As can be seen, the friction coefficient was found to be in the range of 0.35 to 0.52
and the material used (regular concrete versus HPFRC) did not seem to have an effect on
the shear friction coefficient. Table 5-6 lists the value of for all the test walls.
Figure 5-16 presents a plot of the peak shear stress sustained by the specimens versus the
shear friction capacity assuming . A nearly linear increase for the wall shear
strength with an increase in vertical reinforcement strength is observed, as also reported
by Wood (1990). Based on the test results from this study a simple relationship, using
linear regression analysis, was found for the shear strength of the wall specimens as a
function of the vertical reinforcement strength:
(psi) (5-16)
The wall peak shear stress, normalized by (psi), is shown in Fig. 5-17. All the
specimens, except for HPFRC Specimen S2, had shear strengths greater than
(psi), which is the lower limit suggested by Wood (1990) for low-rise walls. It is worth
emphasizing that Specimen S2 was the only HPFRC wall without dowel bars at the wall-
foundation interface, which led to excessive sliding along this section with the associated
loss of stiffness and strength. It can be concluded, therefore, that the use of dowel
reinforcement in HPFRC walls to strengthen the wall-foundation interface is also critical
so that the minimum shear strength of (psi) can be achieved. Nonetheless, the
lower limit of (psi) proposed by Wood for RC low-rise walls was verified by the
results of this study.
Fig. 5-18 shows the envelope (for the first loading cycle at each drift level) of the shear
force normalized by the shear friction strength (for versus the sliding at the
horizontal crack for several of the test walls. The responses shown correspond to the
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average response for the positive and loading direction. The reader should be reminded
that for all the RC specimens and HPFRC Specimen S2 the horizontal crack was
developed at the wall base, whereas for the HPFRC specimens with dowel bars, the crack
was formed in the region where the bonded part of the dowel terminated. The data for
Specimen S1 were not included in the plot because the load versus sliding response was
highly unsymmetrical for the two loading directions (see Fig. 4-23(a)). Also, data were
not available for Specimens S2, S7 and S8 such that the response envelope could be
obtained.
The nearly linear ascending portion of the curves in Fig. 5-18 provides an estimation of
an “elastic sliding stiffness”, which can be normalized by the shear friction strength
assuming µ = 1. Table 5-7 lists the values of normalized elastic sliding stiffness obtained
from the envelope responses shown in Fig. 5-18. The elastic sliding stiffness was
calculated as the secant stiffness at 80% of the shear friction strength. As can be seen, the
experimentally obtained values were relatively consistent (ranging from 7.5/in. to
8.9/in.), although HPFRC Specimens S5 and S10 showed a lower sliding stiffness at the
section where the bonded portion of the dowel bars terminated compared to the sliding
stiffness at the base of the RC walls. Also identified in Fig. 5-18 are discrete values for
the concentrated rotation at the horizontal crack. For concentrated rotations of
approximately 0.15% (0.0015 rad), sliding at the horizontal crack did not exceed 0.05 in.
However, the magnitude of the sliding became greater than 0.1 in. for rotations larger
than 0.35%.
The data plotted in Fig. 5-18 suggest that a shear coefficient of 0.25, as suggested by
Wood (1990), may be adequate to control excessive sliding. In order to evaluate this
possibility, Fig. 5-19 shows a plot of the shear force, normalized by the shear friction
strength (for , versus sliding at the base of the wall (cold joint) for HPFRC
Specimens S5 and S10. The shear friction capacity at the wall base of these two
specimens was higher because of the addition of dowel bars. It can be seen that the peak
normalized shear force at the wall base was approximately 0.25 for both specimens and
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sliding did not exceed 0.06 in. These limited results thus support the use of Wood’s
proposed shear friction coefficient for preventing substantial stiffness degradation due to
shear sliding.
5.4 WALL SLIP VERSUS CRACK WIDTH
For HPFRC Specimens S5 and S10, for which a wide flexural crack and subsequent
sliding developed at the section where the bonded area of the dowel bars ended, it was
possible to obtain a relationship between the magnitude of sliding and the average crack
width using the data from the Optotrak system. Fig. 5-20 presents a plot of “sliding
stiffness”, , (i.e. ratio of average shear stress to horizontal slip) versus average crack
width for these two specimens. In Fig. 5-21, the sliding stiffness was normalized by the
shear friction capacity, for a friction coefficient, , equal to 1.0. A plot of sliding
stiffness (and absolute slip) versus crack width at the edge of the wall tension side is
shown in Figs. 5-22 and 5-23 for Specimen S5 and S10, respectively. As expected,
sliding stiffness decreased as crack width (either average or at wall tension side)
increased. Damage concentration at the horizontal crack was evident for average crack
widths larger than 0.05 in. At this stage, the sliding stiffness value was below 100 ksi/in.,
whereas the normalized sliding stiffness had a value below 0.5 1/in. For the cycles
leading to failure the average crack width was, on average, 0.1 in. Based on the behavior
of these two specimens, it was concluded that once the magnitude of sliding stiffness
decreases below 100 ksi/in., the opening of the horizontal crack and associated sliding
governed the behavior of the specimens. It can also be observed that the width of the
horizontal crack at the wall tension side of Specimen S10 exceeded 0.1 in. only during
the last negative loading half cycle, whereas for Specimen S5 the crack width was larger
than 0.1 in. for drifts above 1.0%.
5.5 SHEAR DISTORTION AND ROTATION INTERACTION
Specimens S7 and S8 were the only walls in the study that were designed to fail by
diagonal tension. Thus, the results from the test of these two specimens were used to
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evaluate the interaction between flexural rotations and shear distortions. A plot of shear
distortion, , versus the shear stress for Specimens S7 and S8 is shown in Figs. 5-24 (a)
and (b), respectively. Because no Optotrak markers were used in these two specimens,
shear distortions were calculated from two diagonal potentiometers (see Fig. 3-29), while
rotations correspond to those at a section 0.3h from the wall base, where h refers to the
wall height excluding the top block. The two specimens exhibited similar behavior and
the shear strain remained below 0.5% for average shear stress less than (psi).
However, shear strains increased significantly in both specimens, particularly in the
loading direction in which a diagonal tension failure ultimately developed (positive and
negative direction for Specimens S7 and S8, respectively). Damage concentration along
the diagonal crack that led to failure was observed for shear strains greater than
approximately 1.0%, and peak shear distortions reached 2.0% when a diagonal tension
failure occurred.
Figs. 5-25 (a) and (b) show a plot between the shear strain and the rotation ratio ( ) in
the lower part of the wall versus average shear stress for HPFRC Specimens S7 and S8,
respectively. Specimens S7 and S8 had ratios below 1.2 up to a shear stress level of
(psi). For the loading direction at which diagonal tension failure ultimately
occurred, the ratio increased rapidly for higher shear stress cycles. This substantial
increase in the ratio indicates a rapid deterioration in shear stiffness that resulted in
degradation of the shear resisting mechanisms.
The shear stress at which a substantial increase of the ratio occurred can be
considered as an upper shear stress limit for use in design of HPFRC low-rise walls.
However, for design purposes, it is useful to determine the contribution of the HPFRC
matrix, , in member shear resistance. Theoretically, the shear stress on the matrix in
every cycle can be estimated as the difference between the total average shear stress
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demand, , and the shear stress contribution from the wall web reinforcement, , as
follows:
(5-17)
Using the readings from the strain gauges attached the web horizontal reinforcement,
was roughly estimated, assuming a diagonal crack with a vertical projection equal to the
wall length. The shear strength contribution from the HPFRC matrix for Specimens S7
and S8 at the peak shear stress demand was found to be (psi). As was mentioned
in Section 3.2, Chompreda and Parra (2007) proposed an HPFRC shear contribution of
(psi) in flexural members, based on cyclic tests of HPFRC beams. An increased
matrix contribution in the case of low-rise walls is expected due to arch action. It should
be noted, however, that the above calculation of matrix contribution in the wall shear
resistance can only be considered an approximation because for low-rise wall vertical
reinforcement may play a more important role that the horizontal reinforcement, as
suggested by many researchers (for example Barda et al., (1977); Cardenas, (1980);
Wood, (1990)) and also verified by the results of this study (see Section 5.3).
Nonetheless, the limit of (psi) for the HPFRC contribution is believed to provide
a reasonable estimate for the design of HPFRC low-rise walls.
5.6 SHEAR STRENGTH AND DRIFT CAPACITY OF TEST SPECIMENS AND
COMPARISON WITH OTHER STUDIES
Fig. 5-26 presents the drift capacity versus peak strength for all the test specimens in this
study. As expected, there is a general trend of a decreasing wall drift with increased shear
stress demand. The HPFRC walls, despite the relaxed reinforcement detailing, exhibited
similar or larger drift capacities compared to the companion RC specimens. It can also be
observed that for the wall specimens in this study, the wall shear span-to-length ratio (1.2
or 1.5) did not seem to have a significant effect on the wall deformation capacity.
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In Section 2.2.2.2, several experimental studies on the behavior of RC low-rise walls
were discussed and a summary of these studies was presented in Tables 2-1 and 2-2. In
order to compare the shear strength and drift capacity of the HPFRC walls with that of
RC walls with similar reinforcement detailing, specimens with the following
characteristics were chosen:
Rectangular wall sections;
Tests with no axial load;
Cantilever wall specimens;
Specimens with no diagonal reinforcement;
Walls with shear span-to-length ratios ranging from 1.0 to 1.5;
Tests with shear stress demands in the range of to (psi).
Walls with no confinement reinforcement or with confinement reinforcement that
did not comply with the 2005 ACI Code requirements for special boundary
elements.
The characteristics of these test specimens, as well as their shear strength and drift
capacity, are summarized in Table 5-8. The RC and HPFRC walls tested in this study
were also included in the table for easy comparison. The specimens in the study by Lefas
et al. (1990) had confinement in the boundary regions that did not comply with the
provision of the 2005 ACI Code, whereas the reinforcing detailing of the walls tested by
Salonikios and al. (1999) followed the provisions of Eurocode EC8. All the low-rise wall
specimens in the studies by Cardenas et al. (1980) (except for specimen SW13), Lefas et
al. (1990), and Maier (1992) were tested under monotonic loading, but they were
included in Table 5-7 because of the similarity in their characteristics with the specimens
of this study. As a result, the drift capacity of these specimens should be considered as an
upper bound, as testing the same specimens under reversed cycle loading would have
likely resulted in reduced drift capacities. This is the case of Specimens SW9 and SW13
in the study by Cardenas et al. (1980), which had the same characteristics but were tested
under monotonic and reversed cyclic loading, respectively. Specimen SW9 sustained a
peak shear stress of (psi) and failed by diagonal compression at a drift of 0.6%.
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On the other hand, Specimen SW13 sustained a lower peak stress ( (psi)) and
failed by diagonal compression, as Specimen SW9, at a drift of approximately 0.5%.
Fig. 5-27 presents a comparison of the shear stress versus drift capacity relationship for
RC specimens (all tested under monotonic loading) with no confinement reinforcement in
the wall boundary regions with that of the HPFRC walls tested in this study (no or little
confinement reinforcement at the wall boundaries). It can be generally observed that the
HPFRC specimens exhibited higher drift capacities when compared to the RC specimens
that had no confinement reinforcement, even though the RC walls were tested under
monotonic loading. For shear stress levels of approximately (psi), the RC wall
with no confinement reinforcement sustained a drift of 1.2%, whereas HPFRC Specimen
S2 exhibited a drift capacity of about 3.0%. For increased shear stress levels, in the range
of (psi), drift capacity for the RC walls ranged between 1.0% and
1.4%, while the drift capacity in the HPFRC specimens ranged between 1.5% and 2.2%.
For high shear stresses (about (psi)), the RC and HPFRC walls sustained similar
drifts, but very limited test data were available for walls with such high shear stress
demands.
It is interesting to discuss the behavior of Specimen SW13 in the study by Cardenas et al.
(1980), tested under displacement reversals, with that of the HPFRC walls of this study.
Specimen SW13 had no confinement reinforcement and web vertical and horizontal
reinforcement ratio equal to 2.8% and 1.0%, respectively. The vertical reinforcement in
this specimen was uniformly distributed and thus, no vertical reinforcement was
concentrated at the wall edges. This specimen was subjected to a peak shear stress
demand equal to (psi) and failed by diagonal compression at a drift of
approximately 0.5%. On the other hand, HPFRC Specimen S5 from this study, with a
similar shear span-to-length ratio, exhibited a drift capacity of 1.5% under a peak shear
stress of (psi). Further, Specimen S10, subjected to a peak shear stress demand of
(psi), exhibited a drift capacity greater than 2.0%.
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Fig. 5-28 presents a plot of shear strength versus drift capacity for all the specimens listed
in Table 5-8. It should be emphasized that except for the specimens tested in this study
and Specimen SW13 by Cardenas et al. (1980), all RC specimens shown in Fig. 5-28
were tested under monotonic loading. A relatively wide scatter can be observed in the
drift capacity of RC walls with no confinement reinforcement (0.5% to 1.9%). Specimens
SW11 and SW12 in the study by Cardenas et al. (1980) showed the largest drift capacity
in this group. These two specimens failed by diagonal tension, but inadequate
development length of the vertical reinforcement in the upper part of the walls was also
reported. RC walls with a volumetric confinement reinforcement ratio of 0.67% and
detailing in the wall boundary regions that did not comply with the 2005 ACI Code
generally exhibited similar drift capacities (in the range of 1% to 1.4%) compared to
those of the RC specimens with no confinement reinforcement. On the other hand, the
HPFRC walls with no confinement reinforcement and shear stress demands of about
(psi) showed similar deformation capacities as the RC walls with 1.0%
volumetric confinement ratio. A confinement reinforcement ratio of 1.0% resulted in an
enhanced drift capacity in the RC walls, with drift capacities in the range 1.5% to 2.4%.
However, specimens with a confinement ratio equal to 1.7% (walls tested by Salonikios
et al., 1999) exhibited an inferior performance in terms of drift capacity. It should be
noted, thought, that these specimens failed by sliding shear at the wall base.
123
CHAPTER 6
SUMMARY AND CONCLUSIONS
6.1 SUMMARY
Reinforced concrete low-rise walls are frequently used as the primary component of the
lateral-load resisting system in low-rise buildings located in earthquake prone regions.
Low-rise walls, usually defined as walls with a height-to-length ratio less than two,
exhibit a behavior highly influenced by shear and find applications in residential
buildings, parking structures, industrial buildings, and nuclear power plants, among
others. The reinforcement detailing in RC structural walls specified in Chapter 21 of the
2008 ACI Code (318 ACI Committee, 2008) typically consists of main vertical
reinforcement at the wall edges, and distributed horizontal and vertical web
reinforcement to provide cracking control and diagonal tension resistance. When large
inelastic deformations are expected, special transverse reinforcement is provided at the
wall edges to increase concrete ductility and to restrain (or delay) buckling of the
longitudinal reinforcement.
The ACI Code required seismic detailing for low-rise structural walls generally ensures
an acceptable level of performance in terms of shear resistance and stiffness, but can
result in severe reinforcement congestion and construction difficulties. In addition, some
experimental studies have revealed inadequate wall deformation capacity and extensive
damage under large shear reversals.
124
In this study, the use of tensile strain-hardening, High-Performance Fiber Reinforced
Concrete (HPFRC) in low-rise walls was experimentally evaluated as a means to simplify
reinforcement detailing and enhance their overall seismic performance and
damagetolerance. The HPFRCs evaluated in this study were reinforced with either
hooked steel fibers in a 1.5% or 2% volume fraction or with ultrahigh molecular weight
polyethylene (Spectra) fibers in a 2% volume ratio.
Nine low-rise wall specimens with shear span-to-wall length ratio of either 1.2 or 1.5 and
shear stress demands ranging from to (psi) were tested under
displacement reversals in the University of Michigan Structures Laboratory. Four of the
specimens were constructed with regular concrete and detailed according to the seismic
provisions of the 2005 ACI Code (318 ACI Committee, 2005). Besides the wall main
flexural reinforcement and the web distributed vertical and horizontal reinforcement,
closely spaced transverse reinforcement was provided in the boundary regions of the
reinforced concrete (RC) walls to avoid early concrete crushing and provide lateral bar
support. On the other hand, the HPFRC low-rise walls had little or no confinement
reinforcement in the boundary regions and the wall distributed reinforcement ratio was
reduced compared with that in the RC walls.
6.2 CONCLUSIONS
From the experiments and analysis conducted in this research, the following conclusions
can be drawn:
1) The RC low-rise walls (shear span-to-length ratio of 1.2 or 1.5) designed according to
the seismic provisions of the 2005 ACI Code (ACI Committee 318, 2005) and tested
under moderate and high shear
stress reversals exhibited a stable hysteretic behavior with drift capacities of
approximately 2.1% and 1.5%, respectively. All the RC specimens exhibited an
opening of the wall-foundation cold joint that led to significant sliding of the wall
during the later stages of the tests. Damage was concentrated in the lower part of the
125
wall and was characterized by either crushing on the extreme compression fibers at the
wall base and vertical splitting cracks in the wall boundary regions (Specimens S1, S6
and S9) or extensive concrete crushing in the wall web (Specimen S4). None of the
RC specimens exhibited a diagonal tension failure.
2) HPFRC walls reinforced with either a 1.5% volume fraction of regular-strength
hooked steel fibers or a 2% volume fraction of Spectra fibers and subjected to
moderate shear stress demands (in the range of showed a
stable hysteretic behavior despite the elimination of the confinement reinforcement in
the wall boundary regions. These walls exhibited drift capacities ranging from 2.1% to
3.0%. In addition, the use of a self-consolidating HPFRC material with a 1.5% volume
fraction of high-strength hooked steel fibers allowed a significant relaxation in the
confinement reinforcement in walls tested under high shear stress reversals (in the
range of ), without compromising wall deformation capacity
(drift capacities ranged between 1.5% and 2.2%). For the HPFRC walls tested under
high shear stress reversals, the confining reinforcing ratio in the wall boundary regions
was one-fourth of that in the companion RC specimens.
3) The RC walls subjected to shear stress demands in the range
showed a concentration of damage in the lower part of the wall for drifts larger than
1.3%. The RC walls tested under high shear stress reversals ,
on the other hand, exhibited significant shear-related damage at drifts of
approximately 1.2%, while concrete spalling initiated during the cycles at drifts
ranging from 1.3% to 1.5%. Compared to the companion RC walls, the HPFRC wall
specimens showed a much denser array of cracks of smaller widths. Only minor shear-
related damage was evident in the walls constructed with an HPFRC material at drifts
below 1.3% and concrete spalling, if any, was not substantial, even at drifts in the
order of 2.0%. The HPFRC specimens therefore exhibited superior damage tolerance
compared to the companion RC specimens.
126
4) Horizontal sliding along the cold joint at the wall base was significant during the later
stages of the test for all the RC walls. However, the wall-foundation interface was
particularly critical in the HPFRC low-rise walls because no fibers bridged that
section, making it susceptible to damage localization and potential sliding shear
failure. This is exacerbated by the excellent bond between reinforcing bars and
HPFRC. The need for reinforcement to strengthen the HPFRC wall-base interface was
clearly demonstrated by the hysteretic behavior of HPFRC Specimen S2, without any
additional reinforcement at the wall base. Despite the low aspect ratio of the wall
(shear span-to-length ratio of 1.2), the concentrated flexural deformations at the wall
base were large enough (approximately equal to 0.008 rad and larger than 0.01 rad at a
drift of 2.3% and 3.0%, respectively) to result in an excessive loss of stiffness and a
subsequent sliding shear failure. Thus, the use of dowel reinforcement is
recommended to strengthen the cold joint at the base of HPFRC low-rise walls in
order to force inelastic deformations to occur within the walls and avoid a premature
sliding shear failure.
5) RC walls tested under moderated shear stress reversals ( to )
sustained drifts that exceeded 2.0%, whereas the increase in the shear stress demand to
stresses above (psi) limited their drift capacity to approximately 1.5%. On the
other hand, the HPFRC low-rise walls exhibited drift capacities equal to or larger than
those of the companion RC specimens. In addition, the variation of wall shear span-to-
length ratio from 1.2 to 1.5 did not seem to have a strong effect on wall deformation
capacity in the case of both RC and HPFRC walls.
6) Moderate shear related damage in RC walls was associated with shear strains varying
between 0.005 rad and 0.007 rad. Only minor shear related damage was evident in the
HPFRC walls at shear distortions of about 0.01 rad and diagonal crack opening was
evident at shear strains greater than 0.015 rad. Specimens S7 and S8, which failed in
diagonal tension, exhibited shear strains of 0.02 rad prior to failure. Based on the
experimental results, the shear distortion capacity of low-rise HPFRC walls can be
conservatively taken as 0.015 rad.
127
7) All the HPFRC specimens had a higher peak-to-peak displacement secant stiffness,
normalized by the specimen secant stiffness at 0.15% drift, compared to the
normalized stiffness of the companion RC specimens at the same drift level. The
stiffness values of the RC and HPFRC walls for the second loading cycle at the same
drift were very close to the first drift cycle values. It was also observed that shear
stress level had an adverse effect on stiffness retention because the RC and HPFRC
specimens tested under moderate shear stress levels ( to ) exhibited
a more gradual loss of stiffness compared to the walls subjected to higher shear stress
demands ( to ).
8) In the RC walls tested under high shear stress reversals (Specimens S4 and S9) the
contribution of rotations (elastic and inelastic) to the total drift was approximately
60% for cycles up to 1% drift. For larger drifts, however, the contribution from
flexural rotations decreased as the slip at the wall base increased (a contribution that
ranged from 30% to 40% of the total drift). For the HPFRC specimens subjected to
high shear stress demands (Specimens S5 and S10), the contribution of shear
distortions to the applied drift increased from 25% for drifts below 1% to 80% and
40% in the cycles leading to failure for Specimens S5 and S10, respectively.
Rotations, mostly concentrated at the wall base, contributed close to 70% of the total
drift at the end of the test for the HPFRC specimen that failed by sliding shear at the
wall base (Specimen S2), whereas this contribution was approximately 50% in the
companion RC specimen (Specimen S1).
9) The plastic hinge length for the RC walls tested under high shear stress reversals
(Specimens S4 and S9) was found to be in the range of , where refers
to the wall height (excluding the top block). The HPFRC specimens designed for the
same shear stress demands (Specimens S5 and S10) exhibited a longer plastic hinge
length (in the range of ). The equation proposed by Pauley and Priestley
(1993) for low-rise walls resulted in longer plastic hinge lengths for these walls
compared to the experimentally estimated values.
128
10) The test results revealed a nearly linear increase in wall shear strength with an
increase in the area of vertical reinforcement, which can be described by the following
equation:
where (in.2) is the area of vertical reinforcement in the wall (wall main and web
vertical reinforcement) and (in.2
) is the wall cross-sectional area. The lower limit
of (psi) for the shear strength of low-rise walls proposed by Wood (1990) was
found to be consistent with the test results, expect for the HPFRC specimen that failed
prematurely by sliding shear (Specimen S2) because of the lack of dowel
reinforcement strengthening the wall-foundation interface.
11) In all the RC wall specimens in which damage concentrated at the wall corners close
to the base (Specimens S1, S6 and S9), the maximum value for the rotation at
from the wall base (where h is the wall height excluding the top block) was found to
be approximately equal to 0.005 rad, regardless of wall shear span-to-length ratio or
shear stress demand.
12) For HPFRC Specimens S7 and S8 that failed by diagonal shear, the ratio of shear
distortion to rotation, , increased gradually and remained below 1.2 for shear stress
levels of up to (psi). For larger shear stresses, this ratio increased at a
substantially faster rate, indicating a rapid deterioration in shear stiffness and a
degradation of the shear resisting mechanisms. For Specimen S7 and S8, the HPFRC
contribution to the wall shear resistance was estimated to be (psi), for the drift
cycle at which the peak shear stress was reached.
Further experimental research, coupled with analytical studies, is needed in the following
areas:
129
1) Evaluation of the behavior of HPFRC walls with shear span-to-length ratios well
below 1.2 when subjected to displacement reversals. In this research, the HPFRC low-
rise walls tested had shear span-to-length aspect ratios of 1.2 and 1.5 and as a result,
the conclusions from this study may not be applicable to walls with much lower aspect
ratios.
2) In this research, only HPFRC materials with either 1.5% or 2% volume fraction of
fibers (hooked steel fibers and Spectra fibers) were evaluated for use in low-rise
structural walls. Thus, the behavior of low-rise walls with lower fiber volume fractions
should be investigated, given the increase in cost associated with the addition of fibers
to the concrete.
3) The results from this study demonstrated the potential for a substantial relaxation in
the confinement reinforcement in the boundary regions of low-rise walls through the
use of HPFRC materials. Further experimental studies, however, are necessary to
determine the minimum amount of required confinement to ensure adequate wall
behavior, based on parameters such as shear stress, wall aspect ratio, and drift demand.
130
Table 2-1 Summary of Tests of Rectangular Low-Rise Reinforced Concrete Structural Walls
Researchers Label Type of loading
Wall Thickness
(in.)
Shear Span-to-Length Ratio
Peak Shear Stress,
in (psi)
Ultimate Drift (1)Failure Mode
(%)
Synge et al. (1980)
Wall 1 Cyclic
4 0.6 6.2 0.85 Sliding shear Wall 2 4 0.6 6.8 0.80 Buckling of diagonal bars
Cardenas et al. (1980)
SW-7
Monotonic
3 1.1 6.6 1.1 Diagonal tension SW-8 3 1.1 7.2 1.5 SW-9 3 1.1 8.6 0.6 Diagonal compression SW-10 3 1.1 4.0 0.7 Diagonal tension SW-11 3 1.1 8.2 1.4 Diagonal tension (2)
SW-12 3 1.1 8.8 1.9 SW-13 Cyclic 3 1.1 8.0 0.5 Diagonal compression
Wiradinata and Saatcioglu
(1986)
Wall 1 Cyclic
4 0.6 6.9 1.75 Diagonal tension
Wall 2 4 0.3 8.9 2.6 Sliding shear
Lefas et al. (1990)
SW11
Monotonic
2.8 1.1 8.2 1.0
Vertical splitting of boundary region
SW12 2.8 1.1 10.7 1.1 SW13 2.8 1.1 11.9 1.1 SW14 2.8 1.1 9.4 1.4 SW15 2.8 1.1 11.2 1.0 SW16 2.8 1.1 11.3 0.7 SW17 2.8 2.1 8.2 1.3 SW21 2.8 2.1 5.5 1.5 SW22 2.8 2.1 6.0 1.0 SW23 2.8 2.1 7.4 1.0 SW24 2.8 2.1 4.9 1.3 SW25 2.8 2.1 6.4 0.6 SW26 2.8 2.1 6.4 1.5
131
Maier (1992)
S4
Monotonic
4 1.2 7.0 1.0 Diagonal compression
S9 4 1.2 6.5 0.9 Diagonal tension S10 4 1.2 12.3 1.1 Diagonal compression
Salonikios et al. (1999; 2000)
MSW1
Cyclic
4 1.5 3.9 (3) 1.5 Buckling of longitudinal bars
MSW2 4 1.5 2.4 (3) 1.9
Sliding shear
MSW3 4 1.5 3.6 (3) 1.4
MSW4 4 1.5 3.2 (3) 1.5
MSW5 4 1.5 4.0 (3) 1.4 MSW6 4 1.5 3.9 (3) 1.5
LSW1 4 1.0 5.6 (3) 0.9
LSW2 4 1.0 4.1 (3) 0.9 LSW3 4 1.0 5.5 (3) 1.3
LSW4 4 1.0 4.8 (3) 0.8
LSW5 4 1.0 5.1 (3) 1.3
Lopes (2000(a); 2000(b)
SW13
) Cyclic
1.8 1.1 9.3 1.1 Web crushing SW16 1.8 1.1 7.2 0.94
Diagonal tension SW17 1.8 1.1 7.4 0.94
SW18 1.8 1.1 8.9 0.96
132
1
Hidalgo et al. (2002) Cyclic
4.8 1.0 4.5 0.93
Diagonal tension
2 4.8 1.0 6.1 1.31 4 4.8 1.0 7.4 1.21 6 4.8 0.7 5.7 0.95 7 4.8 0.7 6.6 1.11 8 4.8 0.7 7.3 1.13 9 4.0 0.7 5.7 1.01 10 3.2 0.7 5.4 0.86 11 4.0 0.5 5.0 0.74 12 4.0 0.5 6.3 0.70 13 4.0 0.5 5.8 0.74 14 3.2 0.35 5.5 0.38 15 3.2 0.35 7.5 0.53 16 3.2 0.35 7.4 0.51 21 4.0 0.7 4.9 NA (3)
22 4.0 0.7 5.0 0.28 23 4.0 0.7 6.3 0.78 24 4.0 0.7 6.1 0.23 25 4.0 0.5 6.2 0.51 26 4.0 0.5 5.4 0.48 27 4.0 0.5 8.6 0.83 28 4.0 0.5 4.6 0.36 29 3.2 0.35 8.3 NA(3) 30 3.2 0.35 8.5 0.57 31 3.2 0.35 8.2 NA(3) 32 3.2 0.35 7.2 NA(3)
133
Choi (2006) SWR1
Cyclic 4.0 0.75 6.1 NA Sliding shear (4)
SWR2 4.0 0.75 6.3 NA Web crushing/Buckling of diagonal reinforcement
(4)
(1) Drift is defined as the ratio of the reported displacement at ultimate condition to the wall shear span (2) Inadequate anchorage development of the straight vertical reinforcement in the upper part of the wall was also reported for the specimen (3) The shear span value was not given in the publication; thus the wall height-to-length ratio is given here (4)
No data were reported for this specimen
134
Table 2-2 Summary of Tests of Barbell and Flanged Low-Rise Reinforced Concrete Structural Walls
Researchers Label Type of loading
Wall Thickness
(in.)
Shear Span-to-Length
Ratio
Peak Shear Stress ,
(psi)
Ultimate Drift (%) Failure Mode
Barda et al. (1977)
B1-2 Monotonic 4 0.5 14.0 0.6
Diagonal tension
B2-1 4 0.5 15.1 0.7 B3-2
Cyclic
4 0.5 13.3 0.6 B4-3 4 0.5 14.5 0.5 B5-4 4 0.5 8.1 0.5 B6-4 4 0.5 11.8 0.6 B7-5 4 0.3 13.9 0.8 B8-5 4 1.0 11.4 0.6
Synge et al. (1980)
Wall 3 Cyclic
4 0.6 6.2 0.35 Sliding shear
Wall 4 4 0.6 6.3 0.60 Buckling of diag. bars
Maier (1992)
S1 Monotonic
4 1.2 11.4 2.1
Diagonal Compression
S2 4 1.2 16.1 1.1 S3 4 1.2 16.5 1.1 S5 Cyclic 4 1.2 11.4 1.5 S6 Monotonic 4 1.2 11.4 1.7 S7 Cyclic 4 1.2 15.0 0.7 S8 Monotonic 4 1.2 9.2 1.1
Sittipunt et al. (2001)
W1
Cyclic
4 1.4 6.5 1.8 Web crushing W2 4 1.4 8.2 1.5 W3 4 1.4 7.4 1.7 Crushing of
flanges W4 4 1.4 8.2 1.8
Choi (2006)
SW4
Cyclic
4 0.75 9.1 NADiagonal tension
(1)
SW5 4 0.75 11.3 NA(1) SW6 4 0.75 9.1 NA Sliding shear (1) SW7 4 0.75 10.2 NA Web crushing (1)
(1) It was not possible to obtain the ultimate drift from the publication.
135
Table 3-1 Main Features of Test Specimens
Specimen (1)
(in. in.) (2)
(in.) (3)
Target Shear
Stress Level (psi)
Mixture
Description
S1 40 40 40 1.2 Regular Concrete
S2 40 40 40 1.2 Mortar with 2.0% volume fraction of Dramix ZP 305
S4
(5)
40 40 40 1.2 Regular Concrete
S5 40 40 40 1.2 Concrete with 1.5% volume fraction of Dramix RC-80/30-BP
S6
(6)
40 40 52 1.5 Regular Concrete
S7 40 40 (4) 52 1.5 Mortar with 2.0% volume fraction of Dramix ZP 305
S8 40 40 (4) 52 1.5 Mortar with 1.5% volume fraction of Spectra Fibers
S9
(7)
40 40 52 1.5 Regular Concrete
S10 40 40 52 1.5 Regular Concrete
(1) : wall thickness; : wall length (2) : wall height (excluding top block) (3) : shear span-to-wall length ratio (4) Specimen tested by Kim and Parra (2003) (5) Dramix ZP 305 fibers: length 1.2 in.; diameter 0.022 in.; tensile strength 160-200 ksi (6) Dramix RC-80/30-BP: length 1.2 in.; diameter 0.015 in.; tensile strength 335 ksi (7) Spectra fibers: length 1.5 in.; diameter 0.0015 in.; tensile strength 375 ksi
136
Table 3-2 Maximum Wall Shear and Calculated Shear Strength of Test Specimens
Specimen
Shear Demand Nominal Shear Strength
Nominal “Concrete” Contribution
Nominal “Steel” Contribution
“Concrete” Contribution Demand
(kips)
(kips)
(1) (kips)
(kips)
(kips)
S1 70.6 6.2 102 9.0 34.0 3.0 68.0 6.0 2.6 0.2
S2 56.9 5.0 86.6 7.6 56.6 5.0 30 (2) 2.6 26.9 2.4
S4 105 9.3 134 11.8 34.0 3.0 100 8.8 5.00 0.5
S5 101 8.9 132 11.7 56.5 5.0 75.6 (2) 6.7 25.4 2.2
S6 87.0 7.7 102 9.0 34.0 3.0 68.0 6.0 19.0 1.7
S7 86.0 7.6 69.0 6.1 56.5 5.0 12.5 (2) 1.1 73.5 6.5
S8 86.0 7.6 69.0 6.1 56.5 5.0 12.5 (2) 1.1 73.5 6.5
S9 108 9.6 114 10.1 34.0 3.0 80.4 7.1 27.6 2.5
S10 96.0 8.5 117 10.3 56.5 5.0 60.0 (2) 5.3 36.0 3.2 (1) Nominal shear strength provided by “concrete” contribution and “shear reinforcement” contribution, i.e. horizontal web reinforcement (2) Assumed contribution based on previous research (see Section 3.2.2)
137
Table 3-3 Nominal Shear Strength for Shear-Transfer at the Wall Base of Test Specimens
Specimen (kips)
(1) (kips)
(2) (kips)
(3)
S1 93.6 93.6 70.6
S2 72.0 72.0 56.9
S4 143 128 105 (4)
S5 174 128 101 (4)
S6 143 128 87 (4)
S7 185 128 86 (4)
S8 185 128 86 (4)
S9 181 128 116 (4)
S10 216 128 97 (4) (1) refers to total vertical reinforcement in the wall, including dowel bars, if any, nominal was taken equal to 60,000 psi for all types of vertical reinforcement, and the shear coefficient, , was taken as 0.6 (2) Nominal shear strength for shear transfer at the wall cold joint (3) Maximum expected base shear (see Table 3-2) (4)
Limit of governed the nominal shear strength for shear transfer
Table 3-4 Extreme Fiber Compressive Stress Corresponding to Maximum Moment for Evaluating Need for Confinement in Boundary Elements According to 2005 ACI Code.
Specimen Stress (psi) (1)
S1 3180
S2 2560
S4 4725
S5 4545
S6 5220
S7 5160
S8 5160
S9 6480
S10 5760 (1) The limit of for the compressive stress is equal to 1000 psi for the design value of equal to 5000 psi
138
Table 3-5 Wall Reinforcement Details
Specimen
Vertical Reinforcement (Boundary Region)
Vertical Reinforcement (web region)
Horizontal Reinforcement
Confinement Reinforcement
(Boundary Region)
Dowel Reinforcement
Bars (1) (2) Bars (3) Bars (4)
S1 4No.4 5.0 0.53 [email protected] in. 0.71 [email protected] in. 0.71 Ø0.162 @ 1.0 in. -
S2 4No.4 5.0 0.53 [email protected] in. 0.31 [email protected] in. 0.31 - -
S4 2No.6+2No.5 9.4 1.0 [email protected] in. 0.83 [email protected] in. 0.83 Ø0.162 @ 1.0 in -
S5 4No.5 7.6 0.82 [email protected] in. 0.63 [email protected] in. 0.63 Ø0.162 @ 1.0 in 4No.4
S6 2No.6+2No.5 9.4 0.98 [email protected] in. 0.71 [email protected] in. 0.71 Ø0.162 @ 4.0 in -
S7 3No.7 7.5 1.1 [email protected] in. 0.21 No.2@10 in. 0.13 (5) - 2No.5
S8 3No.7 7.5 1.1 [email protected] in. 0.21 No.2@10 in. 0.13 (5) - 2No.5
S9 2No.7+2No.6 13.0 1.4 [email protected] in. 0.67 [email protected] in. 0.67 Ø0.162 @ 1.0 in -
S10 4No.6 11.0 1.2 [email protected] in. 0.50 [email protected] in. 0.50 Ø0.162 @ 4.0 in 4No.4
(1) : Boundary region reinforcing ratio (2) : Longitudinal reinforcement in the boundary elements as a tension reinforcement ratio (3) : Vertical reinforcement ratio (4) : Horizontal reinforcement ratio (5) One layer of reinforcement
139
Table 3-6 Mixture Proportions (by Weight) for Regular Concrete and HPFRC Mixtures
Mixture Designation
Portland Cement Sand Coarse
Aggregate Water Fly Ash SP VMA(1) Fiber (2) Type (3)
RC 1 1.55 1.45 0.48 - - - - -
HPFRC-SH 1 2 - 0.48 0.20 - - Dramix ZP305 2.0%
HPFRC-PE 1 1 - 0.5 0.15 - Spectra 1.5% (4)
Self-Consolidating HPFRC 1 2.2 1.2 0.8 0.88 0.005 0.038 Dramix
RC-80/30-BP 1.5% (1) Superplasticizer (2) Viscosity Modifying Agent (3) Volume fraction of fibers (4)
Ultra high molecular weight polyethylene fibers
Table 3-7 Properties of Fibers
Fiber Dramix ZP305 Dramix RC-80/30-BP Spectra
Length (in.) 1.2 1.2 1.5
Diameter (in.) 0.022 0.015 0.0015
Tensile strength (ksi) 160 to 200 335 375
Modulus of elasticity (ksi) 29,000 29,000 17,000
140
Table 3-8 Average Concrete Cylinder Compressive Strength at Test Day (ksi)
Specimen
Wall Beams
Material Average Strength
Bottom Top
S1 Regular concrete 6.7 5.7 6.2
S2 Mortar with 2.0% volume fraction of Dramix ZP 305 fibers
7.0 6.2 6.9
S4 Regular concrete 6.7 5.5 5.1
S5 Concrete with 1.5% volume fraction of Dramix RC-80/30-BP
5.7 3.8 3.7
S6 Regular Concrete 6.8 4.0 6.3
S7 Mortar with 2.0% volume fraction of Dramix ZP 305 fibers
6.8 N/A (1) N/A
S8 Mortar with 1.5% volume fraction of
Spectra fibers 6.3 N/A (1) N/A
S9 Regular concrete 6.2 3.8 3.9
S10 Concrete with 1.5% volume fraction of Dramix RC-80/30-BP
5.5 2.9 5.9 (2)
(1) Compressive strength obtained from in. cylinders (2)
Lower compressive strength due to an error of the ready-mix concrete supplier (see Section 3.3.1.1)
Table 3-9 ASTM 1609 Beam Test Results
Specimen
(1)
First Peak Second Peak P150,0.75
(kips)
(2) P150,3.0
(kips)
(3)
Load
(kips)
Deflection
(in.)
Load
(kips)
Deflection
(in.)
S5 11.2 0.0045 14.4 0.022 13.7 6.6
S10 8.8 0.0053 9.8 0.018 7.9 5.2
(1) All tests conducted on in. beams (2) P150, 0.75: Load at 0.03 in. (0.75 mm) deflection (3)P150, 3.0: Load at 1.2 in. (3 mm) deflection
141
Table 3-10 Steel Strength (ksi)
Specimen Reinforcement Type Average Yield
StressAverage Ultimate
Stress (1)
S1&S2 No.2 95.8 99.7
No.4 74.3 108
S4&S5
D5 91.8 94.6
No.4 66.1 106
No.5 64.4 97.2
No.6 65.8 109
S6
No.2 97.3 98.4
No.5 69.8 103
No.6 71.3 108
S7&S8
No.2 N/A N/A
No.5 70.1 89.3
No.7 72.3 98.3
S9&S10
D4 90.2 95.2
No.4 70.1 99.7
No.6 69.3 106
No.7 67.2 101
(1) The yield stress for the No.2 bars, and the D4 and D5 wire was determined using the 0.2% offset method.
142
Table 4-1 Summary of Test Results
Specimen S1 S2 S4 S5 S6 S7 S8 S9 S10
Peak Load (1)81.5
(kips) 72.7 55.0 62.4 101 107 79.5 77.0 87.9 88.3 82.0 80.3 81.8 82.4 119 116 105 97
Peak Shear Stress (1)
(psi) 510 454 343 390 630 669 495 481 549 552 512 502 511 515 746 726 658 605
Peak Shear Stress (1)
(in , psi) 6.2 5.5 4.1 4.7 7.7 8.2 6.5 6.3 6.7 6.7 6.2 6.1 6.4 6.5 9.5 9.3 8.9 8.2
Drift at Peak Load
(%) (1) 2.0 2.2 1.5 1.7 0.6 0.9 0.9 0.8 1.3 1.6 1.32 1.8 1.8 1.8 1.5 1.0 1.1 0.9
Drift Capacity
(%) (2) 2.4 3.0 1.5 1.5 2.1 2.1 2.2 1.5 2.2
Final drift (1) 2.3 (%) 2.5 3.0 2.9 2.3 2.1 2.3 2.4 2.1 2.2 2.5 2.0 2.3 2.3 2.2 2.1 2.4 2.0
(1) Values correspond to the positive and negative loading directions
(2) Drift Capacity (%) is defined as the maximum drift at which at least 80% of the peak load was sustained in both loading directions. For Specimens S1, S2, S6 and S10 there was no significant loss of strength so the drift capacity listed in the table is the peak average drift applied during the test
143
Table 4-2 Probable Shear Demand Associated with Flexural Failure and Nominal Shear Strength
Specimen Probable Shear Demand, (1)
(kips) Nominal Shear Strength, (2)
(kips)
S1 72.1 149
S2 57.2 107 (3)
S4 108 161
S5 91 150 (3)
S6 88.6 150
S7 87.0 78.1 (3)
S8 87.0 78.1 (3)
S9 109 135
S10 90.4 131 (3) (1) Shear demand corresponding to moment capacity at the wall base, calculated based on actual material properties and nonlinear section analysis (2) Nominal shear strength calculated using actual steel yield strength and concrete strength, based on the modified truss analogy (3) HPFRC concrete contribution to shear strength assumed equal to (psi) (see Section 3.2.2)
144
Table 4-3 Load-Displacement History for Specimen S1 Cycle Load (kips) Drift (%)
1 -15.1 -0.14 10.2 0.02
2 -8.3 -0.09 10.2 0.02
3 -14.4 -0.17 17.2 0.08
4 -14.9 -0.17 14.4 0.06
5 -32.4 -0.34 28.3 0.23
6 -27.6 -0.33 28.5 0.23
7 -38.3 -0.51 42.3 0.36
8 -37.6 -0.57 43.3 0.35
9 -43.4 -0.75 55.6 0.52
10 -43.5 -0.79 55.7 0.52
11 -52.1 -0.92 72.1 0.73
12 -49.1 -0.93 64.7 0.73
13 -63.3 -1.21 76.6 0.95
14 -61.9 -1.2 74.7 0.99
15 -68.4 -1.5 79.5 1.2
16 -63.1 -1.4 77.1 1.2
17 -69.6 -1.7 80.5 1.5
18 -68.0 -1.7 76.4 1.4
19 -70.4 -1.9 81.0 1.8
20 -72.7 -2.2 81.5 2.0
21 -63.0 -2.5 60.00 2.3
145
Table 4-4 Load-Displacement History for Specimen S2 Cycle Load (kips) Drift (%)
1 -9.8 -0.12 7.8 0.07
2 -3.8 -0.07 9.3 0.12
3 -12.9 -0.15 15.2 0.21
4 -13.2 -0.19 12.2 0.20
5 -35.6 -0.47 25.3 0.46
6 -34.4 -0.48 20.7 0.44
7 -48.1 -0.66 33.1 0.64
8 -47.1 -0.71 30.9 0.69
9 -55.2 -0.91 45.9 0.95
10 -47.2 -0.87 46.6 1.0
11 -59.1 -1.2 53.1 1.3
12 -56.2 -1.2 49.8 1.3
13 -60.3 -1.4 55.0 1.5
14 -58.8 -1.5 49.7 1.5
15 -62.4 -1.7 53.5 1.7
16 -52.0 -1.7 48.0 1.7
17 -62.2 -2.0 49.3 2.0
18 -58.1 -1.9 41.1 1.9
19 -60.9 -2.2 43.0 2.3
20 -60.5 -2.9 46.3 3.0
146
Table 4-5 Load-Displacement History for Specimen S4 Cycle Load (kips) Drift (%)
1 11.1 0.04 -9.9 0.00
2 10.2 0.05 -9.5 0.01
3 20.9 0.23 -25.1 0.23
4 20.8 -0.08 -18.9 -0.02
5 40.0 0.23 -37.6 -0.08
6 39.7 0.24 -36.8 -0.08
7 60.8 0.34 -58.5 -0.19
8 63.8 0.36 -61.5 -0.22
9 81.8 0.44 -85.9 -0.37
10 80.9 0.45 -85.5 -0.38
11 98.3 0.56 -95.2 -0.55
12 89.1 0.58 -99.9 -0.59
13 97.2 0.77 -102 -0.92
14 90.1 0.87 -94.7 -0.83
15 92.9 1.0 -95.4 -1.0
16 85.4 1.0 -94.5 -1.0
17 95.6 1.3 -95.2 -1.3
18 84.9 1.3 -88.5 -1.3
19 87.3 1.5 -83.5 -1.6
20 65.4 1.9 -53.9 -2.1
21 26.4 2.3
147
Table 4-6 Load-Displacement History for Specimen S5 Cycle Load (kips) Drift (%)
1 10.6 0.04 -9.9 -0.04
2 7.1 0.04 -7.1 -0.03
3 15.2 0.10 -15.4 -0.06
4 15.6 0.11 -15.4 -0.05
5 27.4 0.24 -32.6 -0.17
6 32.4 0.29 -30.4 -0.14
7 39.3 0.36 -43.8 -0.29
8 41.3 0.37 -44.0 -0.28
9 53.4 0.50 -55.3 -0.43
10 49.9 0.45 -53.3 -0.44
11 69.1 0.63 -71.4 -0.62
12 68.2 0.63 -68.0 -0.61
13 73.2 0.86 -76.1 -0.79
14 77.8 1.1 -73.2 -0.84
15 70.5 1.1 -74.4 -1.1
16 68.5 1.1 -69.5 -1.1
17 68.0 1.4 -67.7 -1.4
18 62.0 1.4 -62.1 -1.4
19 59.1 1.6 -58.4 -1.7
20 52.7 1.9 -51.8 -2.0
21 42.3 2.3 -40.6 -2.4
148
Table 4-7 Load-Displacement History for Specimen S6 Cycle Load (kips) Drift (%)
1 11.6 0.04 -12.5 -0.08
2 12.7 0.05 -12.8 -0.07
3 20.6 0.12 -20.8 -0.15
4 23.8 0.14 -22.0 -0.16
5 37.5 0.29 -36.7 -0.31
6 41.7 0.29 -39.6 -0.33
7 53.9 0.43 -55.3 -0.51
8 54.5 0.44 -54.6 -0.50
9 72.2 0.58 -70.5 -0.70
10 69.2 0.59 -71.2 -0.69
11 80.0 0.81 -81.7 -0.95
12 76.5 0.83 -80.7 -0.94
13 81.6 1.0 -87.0 -1.2
14 79.5 1.1 -83.7 -1.2
15 81.8 1.3 -88.4 -1.4
16 80.2 1.3 -79.2 -1.4
17 81.1 1.6 -86.3 -1.6
18 77.6 1.6 -75.6 -1.6
19 77.9 1.8 -86.0 -1.9
20 74.1 2.1 -77.3 -2.2
149
Table 4-8 Load-Displacement History for Specimen S7 Cycle Load (kips) Drift (%)
1 13.0 0.09 -10.0 -0.08
2 13.0 0.09 -10.4 -0.08
3 21.3 0.18 -18.0 -0.21
4 22.4 0.18 -17.3 -0.20
5 31.8 0.27 -24.0 -0.29
6 31.0 0.27 -23.4 -0.29
7 43.1 0.39 -31.0 -0.41
8 41.4 0.39 -29.6 -0.40
9 61.3 0.57 -44.0 -0.61
10 60.1 0.57 -44.3 -0.62
11 75.8 0.77 -57.0 -0.84
12 73.6 0.81 -65.1 -0.92
13 75.3 1.1 -69.0 -1.1
14 74.9 1.0 -70.3 -1.1
15 77.8 1.3 -73.3 -1.3
16 73.9 1.3 -72.9 -1.3
17 76.6 1.5 -75.8 -1.5
18 75.2 1.6 -75.0 -1.5
19 75.1 1.8 -76.4 -1.8
20 72.2 1.8 -75.4 -1.8
21 64.8 2.1 -75.4 -2.0
22 39.9 2.4
150
Table 4-9 Load-Displacement History for Specimen S8 Cycle Load (kips) Drift (%)
1 14.0 0.11 -12.1 -0.07
2 13.2 0.11 -12.3 -0.08
3 20.3 0.20 -19.7 -0.18
4 20.4 0.20 -19.5 -0.18
5 28.2 0.29 -272 -0.26
6 27.6 0.30 -26.4 -0.26
7 33.6 0.41 -32.8 -0.36
8 35.2 0.40 -32.8 -0.36
9 46.9 0.61 -44.0 -0.55
10 48.9 0.61 -44.1 -0.56
11 63.4 0.84 -57.3 -0.78
12 64.7 0.81 -58.6 -0.84
13 74.8 1.07 -64.5 -0.98
14 72.2 1.1 -66.4 -1.0
15 75.1 1.0 -68.8 -1.1
16 74.5 1.3 -70.3 -1.2
17 75.5 1.3 -71.2 -1.2
18 76.3 1.6 -82.4 -1.8
19 76.2 1.5 -62.0 -1.5
20 75.6 1.8 -69.6 -1.8
21 77.2 1.82 -70. -1.8
22 75.9 2.0 -69.8 -2.0
23 74.3 2.3 -50.8 -2.3
151
Table 4-10 Load-Displacement History for Specimen S9 Cycle Load (kips) Drift (%)
1 -12.6 -0.01 15.1 0.02
2 -14.4 -0.01 16.1 0.02
3 -20.9 -0.02 26.8 0.05
4 -28.3 -0.03 26.4 0.05
5 -53.5 -0.11 49.2 0.12
6 -50.4 -0.12 51.2 0.14
7 -81.3 -0.22 66.1 0.21
8 -77.9 -0.22 65.1 0.21
9 -99.3 -0.30 91.9 0.32
10 -96.0 -0.31 85.8 0.31
11 -109 -0.49 103 0.39
12 -108 -0.49 103 0.40
13 -111 -0.70 113 0.67
14 -106 -0.72 109 0.66
15 -109 -0.98 113 0.91
16 -103 -0.97 108 0.94
17 -106 -1.2 110 1.3
18 -96.7 -1.2 94.4 1.3
19 -95.7 -1.5 94.9 1.5
20 -84.0 -1.8 87.5 1.9
21 -70.4 -2.1 72.2 2.2
152
Table 4-11 Load-Displacement History for Specimen S10 Cycle Load (kips) Drift (%)
1 -11.9 -0.11 10.9 0.03
2 -11.7 -0.03 9.8 0.03
3 -17.7 -0.06 20.5 0.07
4 -19.0 -0.07 29.0 0.09
5 -32.0 -0.15 43.3 0.18
6 -32.1 -0.15 42.3 0.17
7 -48.1 -0.25 59.0 0.29
8 -48.9 -0.25 60.2 0.30
9 -65.9 -0.35 74.6 0.41
10 -70.3 -0.36 74.1 0.42
11 -84.6 -0.43 88.5 0.66
12 -82.1 -0.47 87.6 0.61
13 -88.7 -0.62 91.7 0.80
14 -84.7 -0.63 90.7 0.76
15 -90.3 -0.90 98.5 1.1
16 -93.1 -1.1 93.7 1.1
17 -86.5 -1.0 94.8 1.2
18 -88.7 -1.1 93.7 1.2
19 -90.0 -1.3 97.3 1.5
20 -89.8 -1.5 94.3 1.8
21 -87.8 -1.8 95.7 2.1
22 -87.0 -2.0 90.3 2.4
153
Table 4-12 Initial Values for Secant Peak-to-Peak Displacement Stiffness and Corresponding Drifts
Specimen Stiffness (kip/in.)
Drift (1)
(%)
S1 260 0.10
S2 160 0.14
S4 530 0.13
S5 310 0.14
S6 260 0.10
S7 170 0.15
S8 180 0.15
S9 720 0.10
S10 480 0.14 (1) The drift value listed refers to the average drift in the cycle for which the secant stiffness was calculated
154
Table 5-1 Theoretical Yield Curvature Based on Section Modeling
Specimen (rad/in.)
S4
S5
S9
S10
Table 5-2 Plastic Hinge Length
Specimen
Plastic Hinge Length,
Pauley and Priestley (1993) Experimental
(in.) (1) (in.) (1)
S4 (RC) 9.8 0.25
6.6 0.16
S5 (HPFRC) 8.7 0.22
S9 (RC) 10.3 0.20
5.8 0.11
S10 (HPFRC) 7.9 0.15 (1)
is the wall height (in.) excluding the top block
Table 5-3 Stress-Strain Values for Modeling of Regular Concrete (Specimens S4 and S9) and HPFRC (Specimens S5 and S10) Tensile Behavior
Matrix
Regular Concrete 450 0.00008 0 0.00008 - - - -
HPFRC 400 0.0001 500 0.005 200 0.015 100 0.02
155
Table 5-4 Compression Stress-Strain Model for Regular Concrete (Specimens S4 and S9) and HPFRC (Specimens S5 and S10) Matrix
Matrix (psi)
Regular concrete 6300 0.003 150 0.008
HPFRC 5600 0.006 100 0.01
Table 5-5 Compressive Strains at Wall Edge in RC Specimens
Compressive Strain
Specimen S4 (1)
Specimen S9
1.0% drift 1.5% drift 2.0% drift (5) 1.0% drift 1.5% drift 2.0% drift (5)
(2) 0.0043 0.0055 0.0061 0.0028 0.0039 0.0085 (6)
(3) 0.001 0.0018 0.0026 0.0016 (7) 0.0028 N/A (7) (8)
(4) 0.00036 0.00040 0.00048 0.0040 (7) 0.00029 0.00026 (1) Strain refers to the average compression strain calculated for the positive and negative loading direction, unless otherwise noted (2) Average compressive strain measured at wall edge from 0 in. to 4 in. from the wall base (3) Average compressive strain measured at wall edge from 4 in. to 9 in. from the wall base (4) Average compressive strain measured at wall edge from 9 in. to 14 in. from the wall base (5) For Specimens S4 and S9, the wall drift capacity was 1.5% (6) Strain refers only to the positive loading direction (7) Strain refers only to the negative loading direction (8)
Concrete spalling at the wall edge affected the readings of some Optotrak markers and a reasonable estimated for the compressive strain could not be obtained
156
Table 5-6 Friction Coefficient Values Based on Test Results
Specimen Calculated Shear Friction Coefficient,
S1 0.52
S2 0.52
S4 0.42
S5 0.39
S6 0.37
S7 0.35
S8 0.35
S9 0.39
S10 0.41
Table 5-7 Elastic Sliding Stiffness Normalized by Shear Friction Strength (µ = 1)
Specimen Normalized Elastic Sliding Stiffness
S4 8.9
S5 7.1
S6 8.2
S9 7.8
S10 7.5
157
Table 5-8 Comparison of test results with other studies
Researcher
(1)
Specimen (4)
(%) (5)
(%) (6)
(%) (7) in
(psi)
Drift capacity
(%)
Cardenas et al. (1980)
SW-7 1.1 (2) 1.0 0.27 - 6.6 1.1 SW-8 1.1 (2) 2.8 0.27 - 7.2 1.5 SW-9 1.1 (2) 2.8 1.0 - 8.6 0.6 SW-10 1.1 (2) - - - 4.0 0.7 SW-11 1.1 (2) - 0.75 - 8.2 1.4 SW-12 1.1 (2) - 1.0 - 8.8 1.9 SW-13 1.1 (3) 2.8 1.0 - 8.0 0.5
Lefas et al. (1990)
SW11 1.1 (2) 2.4 1.1 0.67 8.2 (8) 1.0 SW14 1.1 (2) 2.4 1.1 0.67 9.4 (8) 1.4 SW17 1.1 (2) 2.4 1.1 0.67 8.2 (8) 1.3
Maier (1992)
S4
1.2 (2) 1.0 1.0 - 7.0 1.0 S9 1.2 (2) 1.0 - - 6.5 1.4
S10 1.2 (2) 1.0 0.98 - 12 1.3
Salonikios et al. (1999)
MSW1 1.5 (3) 0.57 0.57 1.0 3.9 (9) 1.5 MSW2 1.5 (3) 0.28 0.28 1.0 2.4 (9) 1.9 MSW6 1.5 (3) 0.57 0.57 1.7 3.9 (9) 1.6 LSW1 1.0 (3) 0.57 0.57 1.7 5.6 (9) 0.9 LSW2 1.0 (3) 0.28 0.28 1.7 4.1 (9) 0.9
This study
S1 1.2 (3) 0.71 0.71 1.0 5.9 2.4 S2 1.2 (3) 0.31 0.31 - 4.4 3.0 S4 1.2 (3) 0.83 0.83 1.0 7.9 1.5 S5 1.2 (3) 0.63 0.63 0.25 6.4 1.5 S6 1.5 (3) 0.71 0.71 1.0 6.7 2.1 S7 1.5 (3) 0.21 0.13 - 6.2 2.1 S8 1.5 (3) 0.21 0.13 - 6.5 2.2 S9 1.5 (3) 0.67 0.67 1.0 9.4 1.5
S10 1.5 (3) 0.50 0.50 0.25 8.6 2.2 (1) See also Tables 2-1 and 2-2 for more information on the test specimens (2 )Monotonic loading tests (3) Cyclic loading tests (4) : wall shear span-to-length (5) : web vertical reinforcement ratio (6) : web horizontal reinforcement ratio (7) : ratio of volume of confinement reinforcement to volume of concrete core in wall boundary elements (8) Approximate value of confinement reinforcing ratio as exact information could not be obtained from the publication (does not comply with 2005 ACI Code provisions for special boundary elements) (9) Confinement in the boundary region followed the provisions of Eurocode EC8 but the detailing did not comply with Eurocode EC8 provisions (10)
Inadequate anchorage development of the straight vertical reinforcement in the upper part of the wall was also reported for the specimen
158
Fig. 1-1 Typical Reinforcement Detailing in the Boundary Regions of Reinforced Concrete Structural Walls (courtesy of Andres Lepage)
159
(a) Typical Diagonal Tension Failure (b) Diagonal Tension in a Steep Failure Plane
(c) Typical Diagonal Compression Failure d) Concrete Crushing in the Wall Web
Fig. 2-1 Shear Failure Modes in RC Low-Rise Structural Walls (Paulay et al., 1982)
160
(a) (b)
(c)
Fig. 2-2 Development of Sliding Shear Mechanism in RC Low-Rise Walls (Paulay et al., 1982)
161
Fig. 2-3 Reinforcing Detailing for the Wall Specimens Tested by Cardenas et al. (1980)
162
(a) Dimensions of Specimens (in mm) (b) Diagonal Reinforcement Layout
Fig. 2-4 Low-Rise Wall Specimen Details in the Study by Paulay et al. (1982)
Fig. 2-5 Geometry of Test Specimens by Wiradinata and Saatcioglu (1986)
Dimensions in mm
163
(a) Specimen W1
(b) Specimen W3
Fig. 2-6 Reinforcement Layout in the Wall Specimens Tested by Sittupunt et al. (2001)
Fig. 2-7 Test Set-Up for Low-Rise Wall Specimens used by Hidalgo et al. (2002)
164
Fig. 2-8 Wall Test Set-Up by Lopes (2000(a)
)
Fig. 2-9 Tensile Stress-Strain Behavior of HPFRCCs (Naaman, 1998)
Dimensions in mm
165
Fig. 2-10 Coupling Beam Specimens in the Study by Canbolat et al. (2005)
166
(a) Wall Height-to-Length Ratio of 1.0 (Shear Span-to-Length ratio of 1.2)
(b) Wall Height-to-Length Ratio of 1.3 (Shear Span-to-Length Ratio of 1.5)
Fig. 3-1 Dimensions of Test Specimens
BOTTOM BEAM(RC)
72
24
40
4016
4
2440
16
24
TOP BEAM(RC)
WALL(RC or HPFRC)
All dimensions in inches
1652
40
72
24
BOTTOM BEAM(RC)
TOP BEAM(RC) 16
5224
24
4
WALL(RC or HPFRC)
All dimensions in inches
167
Fig. 3-2 Reinforcement Details for Bottom and Top Block in Specimens S1, S2, S6, S7 and S8
24
2472
24
16
16
52
16
A
A
B
B
Section A-A
Top Beam Section B-B
6 6 6
No.5 bars
3
4No.6 bars
7 No.6 bars
4 No.6 bars
Bottom Beam
All dimensions in inches
2 No.4 hoops @4 in.
No.4 hoops @4 in.
168
Fig. 3-3 Reinforcement Details for Bottom and Top Block in Specimens S4, S5, S9 and S10
24
2472
24
16
16
60
16
A
A
B
B
Bottom Beam Section A-A
Top Beam Section B-B
6 6 6
3
All dimensions in inches
6 No.6 bars
2 No.4 hoops @4 in.
7No.6 bars
No.4 hoops @4 in.4No.6 bars
No.5 bars
169
Fig. 3-4 Reinforcement Layout in Specimen S1
2440
16
80
52
72 24
16
4
80
1640
24
40
A
B B
A
4No.4 bars
Ø0.162 @1 in.
No.2 @3.5 in.
Elevation Section A-A
4
12
1
40
1 2 34 12
Section B-B
All dimensions in inches
170
Fig. 3-5 Reinforcement Layout in Specimen S2
2440
16
8052
72 24
16
4
80
1640
24
40
AA
BB
Elevation Section A-A
4No.4 bars
No.2 @ 8 in.
4
12
1
40
1 2 34 12
Section B-B
All dimensions in inches
171
Fig. 3-6 Reinforcement Layout in Specimen S4
2440
16
80
52
72 24
16
4
80
1640
24
40
AA
BB
Elevation
D5 @ 3 in.
2No.5 bars
2No.6 bars
Ø0.162 @ 1 in.
Section A-A
4
12
1
40
2 2 33 22
Section B-B
All dimensions in inches
172
Fig. 3-7 Dowel Reinforcement in Specimen S5
Fig. 3-8 Sleeves in Dowel Reinforcement (Specimen S10)
173
Fig. 3-9 Reinforcement Layout in Specimen S5
2440
16
8052
72 24
16
4
80
1640
24
40
86
Sleeves
Elevation Section A-A
D5 @ 4 in.
4No.5 bars
4No.4 bars
Ø0.162 @ 4 in.
A
BB
A
4
12
1
40
2 2 33 22
Section B-B
All dimensions in inches
174
Fig. 3-10 Reinforcement Layout in Specimen S6
2452
16
9252
72 24
16
4
92
1652
24
40A
A
B B
Elevation Section A-A
No.2 @ 3.5 in.
2No.6 bars
2No.5 bars
Ø0.162 @ 1 in.
4
12
1
40
1 2 34 12
Section B-B
All dimensions in inches
175
Fig. 3-11 Reinforcement Layout in Specimens S7 and S8
2452
16
9252
72 24
16
4
92
1652
24
40A
A
BB
Section A-AElevation
No.2 @ 3.5 in.
3No.7 bars
2No.5 bars
4
2
40
3 2 26 322 2
Section B-B
All dimensions in inches
176
Fig. 3-12 Reinforcement Layout in Specimen S9
2452
16
9252
72 24
16
4
92
1652
24
40A
A
BB
Elevation
D4 @ 3.0 in.
2No.7 bars
2No.6 bars
Ø0.162 @ 1 in.
Section A-A
4
12
1
40
2 2 33
11
2
22
Section B-B
All dimensions in inches
177
Fig. 3-13 Reinforcement Layout in Specimen S10
2452
16
9252
72 24
16
4
92
1652
24
40
Sleeves
108
A
BB
A
Elevation Section A-A
4No.6 bars
4No.4 bars
Ø0.162 @ 4 in.
D4 @ 4 in.
4
12
1
40
2 2 331
12
22
Section B-B
All dimensions in inches
178
(a) 5 Cubic Feet Mixer (b) 1.5 Cubic Feet Mixer
Fig. 3-14 Laboratory Concrete Mixers
(a) Dramix Fiber
(b) Spectra (PE) Fiber
Fig. 3-15 Fibers Used in this Study (Naaman, 1999)
179
(c) Crimped Wire (D4) (d) Deformed Wire (D5)
Fig. 3-16 Wire Used in Specimens S4, S5, S9 and S10
Fig. 3-17 ASTM 1609 Beam Test Set-Up
180
(a) Batch 1 (b) Batch 2
Fig. 3-18 Load versus Deflection Response for ASTM 1609 Beam Specimens (Specimen S5)
(a)Batch 1 (b) Batch 2
Fig. 3-19 Load versus Deflection Response for ASTM 1609 Beam Specimens (Specimen S10)
0 0.02 0.04 0.06 0.08 0.1 0.120
2
4
6
8
10
12
14
16
Deflection (in.)
Forc
e (k
ips)
0 0.02 0.04 0.06 0.08 0.1 0.120
2
4
6
8
10
12
14
16
Deflection (in.)
Forc
e (k
ips)
0 0.02 0.04 0.06 0.08 0.1 0.120
2
4
6
8
10
12
14
16
Deflection (in.)
Forc
e (k
ips)
0 0.02 0.04 0.06 0.08 0.1 0.120
2
4
6
8
10
12
14
16
Deflection (in.)
Forc
e (k
ips)
181
Fig. 3-20 Tensile Stress versus Strain Response for D4 Crimped Wire (Three Coupons)
Fig. 3-21 Base Block inside Formwork (Specimen S4)
0 0.005 0.01 0.015 0.020
20
40
60
80
100
120
Strain (in/in)
Stre
ss (k
si)
182
Fig. 3-22 Base Block Ready for Casting (Specimen S10)
Fig. 3-23 Elevation View of Wall Reinforcement Layout (Specimen S10)
183
Fig. 3-24 Wall Ready for Casting (Specimen S10)
Fig. 3-25 Bottom Beam and Wall after Removal of Formwork (Specimen S4)
184
Fig. 3-26 View of Top Beam inside Formwork (Specimen S9)
Fig. 3-27 Completed Specimen (Specimen S6)
185
Fig. 3-28 Instrumentation Scheme for Specimens with Shear Span-to-Length Ratio of 1.2
East West
Loading Direction
1640
24
72
27
23 27
P1 P2P6P5
P3
P4
P11
P12
P13CL3
CL2
CL1
P7 P8
29
12P10 P9
27
12
2
12
2
24
44
24
SIDE VIEWSIDE VIEW
48
ELEVATION VIEW
All dimensions in inchesP = PotentiometerCL = Clinometer
186
Fig. 3-29 Instrumentation Scheme for Specimens with Shear Span-to-Length Ratio of 1.5
East West
Loading Direction
1652
24
72
27
23 27
P1 P2P6P5
P3
P4
P11
P12
P13CL3
CL2
CL1
P7 P8
29
16
P10 P9
27
16
2
16
2
24
44
24
ELEVATION VIEW SIDE VIEWSIDE VIEW
CL4
44
8
P = PotentiometerCL = Clinometer All dimensions in inches
187
Fig. 3-30 Optotrak System Markers Grid
2416
72
Loading Direction
EastWest
5
52.5 35 2.5
34
52 (o
r 40)
Optotrak marker
All dimensions in inches
188
Fig. 3-31 Instrumentation Scheme with Potentiometers and Clinometers
Fig. 3-32 Optotrak Instrumentation Scheme
189
Fig. 3-33 Lateral Bracing Scheme (Specimen S10)
Fig. 3-34 Specimen S4 before Testing
190
Fig. 3-35 Test Set-Up for Specimen S9
Steel Column
Reaction Wall
Connector for Actuator
Actuator
Strong Floor 2452
16
40
Steel Rods
Top Beam
Wall
Bottom Beam
Steel Plate
1-14 in. steel plate
84
1-12 in. rods
1616
Loading DirectionEast West
All dimensions in inches
191
191
Fig. 3-36 Lateral Displacement History
0 5 10 15 20-3
-2
-1
0
1
2
3
Cycle
Drif
t (%
)
192
Fig. 4-1 Calculation of Wall Lateral Displacement
Fig. 4-2 Lateral Force versus Top-Block Displacement Envelope for Specimen S5
-2 -1 0 1 2
-100
-80
-60
-40
-20
0
20
40
60
80
100
Top-Block Displacement (in.)
Late
ral F
orce
(kip
s)
Optotrak markersActuator LVDT
193
Lower Strip (used for calculation of slip)
Fig. 4-3 Calculation of Shear Strain (adapted from Sittipunt and Wood, 1995)
Fig. 4-4 Definition of “Longitudinal Strips” in Wall Specimen
Strip 5
Strip 4
Strip 3
Strip 2
5 in.
35 in.
v1
u1
d’1
d’2 d1
d2
v2
u2
H
L
25 in.
Strip 1
194
2
1 4
3
u2
v2
v3
u3
u1
v1
u4
v4
β1
β2
β3
β4
Fig. 4-5 Deformation of a Quadrilateral Element for Calculation of Average Strains
195
(a) 1.0% drift
(b) 2.3% drift (end of test)
Fig. 4-6 Cracking Pattern in Specimen S1
196
(c) close-up of damage in boundary region at the base of wall (2.3% drift)
Fig. 4-6 Cracking Pattern in Specimen S1
(a) 1.0% drift
Fig. 4-7 Cracking Pattern in Specimen S4
197
(b) 1.9% drift
(c) 2.4% drift (end of test)
Fig. 4-7 Cracking Pattern in Specimen S4
198
(a) 0.9% drift
(b) 2.1% drift (end of test)
Fig. 4-8 Cracking Pattern in Specimen S6
199
(c) close-up of wall boundary region at end of test (2.1% drift)
Fig. 4-8 Cracking Pattern in Specimen S6
(a) 1.0% drift
Fig. 4-9 Cracking Pattern in Specimen S9
200
(b) state of damage in wall boundary region at 1.8% drift
(c) 2.2% drift (end of test)
Fig. 4-9 Cracking Pattern in Specimen S9
201
(a) 1.2% drift
(b) first observed vertical splitting cracks at a drift of 1.5%
Fig. 4-10 Cracking Pattern in Specimen S2
202
(c) 3.0% drift (end of test)
(d) close-up of boundary region after end of test (3.0% drift)
Fig. 4-10 Cracking Pattern in Specimen S2
203
(a) 0.85% drift
(b) 1.3% drift
Fig. 4-11 Cracking Pattern in Specimen S5
Section where bonded region of dowel bars
terminated
204
(c) 1.9% drift
(d) 2.4% drift (end of test)
Fig. 4-11 Cracking Pattern in Specimen S5
205
(a) 1.0% drift
(b) 2.4% drift (end of test)
Fig. 4-12 Cracking Pattern in Specimen S7
End-line of dowel bars
206
(a) 1.0% drift
(b) 2.1% drift
Fig. 4-13 Cracking Pattern in Specimen S8
207
(a) 1.0% drift
(b) 1.4% drift
Fig. 4-14 Cracking Pattern in Specimen S10
208
(c) 1.9% drift
(d) 2.2 % drift (end of test)
Fig. 4-14 Cracking Pattern in Specimen S10
Section where bonded region of dowel bars
terminated
209
(a) Specimen S1
(b) Specimen S2
Fig. 4-15 Load versus Drift Response
-3 -2 -1 0 1 2 3-180
-140
-100
-60
-20
20
60
100
140
180180
Drift (%)
Late
ral F
orce
(kip
s) Vpr
Vn
Vpr
Vn
-3 -2 -1 0 1 2 3-180
-140
-100
-60
-20
20
60
100
140
180
Drift (%)
Late
ral F
orce
(kip
s) Vpr
Vpr
Vn
Vn
210
(c) Specimen S4
(d) Specimen S5
Fig. 4-15 Load versus Drift Response
-3 -2 -1 0 1 2 3-180
-140
-100
-60
-20
20
60
100
140
180180
Drift (%)
Late
ral F
orce
(kip
s)
Vpr
Vpr
Vn
Vn
-3 -2 -1 0 1 2 3-180
-140
-100
-60
-20
20
60
100
140
180180
Drift (%)
Late
ral F
orce
(kip
s)
Vpr
Vpr
Vn
Vn
211
(e) Specimen S6
(f) Specimen S7
Fig. 4-15 Load versus Drift Response
-3 -2 -1 0 1 2 3-180
-140
-100
-60
-20
20
60
100
140
180180
Drift (%)
Late
ral F
orce
(kip
s)
Vpr
Vpr
Vn
Vn
-3 -2 -1 0 1 2 3-180
-140
-100
-60
-20
20
60
100
140
180180
Drift (%)
Late
ral F
orce
(kip
s)
Vpr
Vpr
Vn
Vn
212
(g) Specimen S8
(h) Specimen S9
Fig. 4-15 Load versus Drift Response
-3 -2 -1 0 1 2 3-180
-140
-100
-60
-20
20
60
100
140
180
Drift (%)
Late
ral F
orce
(kip
s)
Vpr
Vpr
Vn
Vn
-3 -2 -1 0 1 2 3-180
-140
-100
-60
-20
20
60
100
140
180
Drift (%)
Late
ral F
orce
(kip
s)
Vpr
Vpr
Vn
Vn
213
(i) Specimen S10
Fig. 4-15 Load versus Drift Response
Fig. 4-16 Comparison of Shear Stress versus Drift Response for Specimens S9 and S10
-3 -2 -1 0 1 2 3-180
-140
-100
-60
-20
20
60
100
140
180180
Drift (%)
Late
ral F
orce
(kip
s)
Vpr
Vpr
Vn
Vn
-3 -2 -1 0 1 2 3-10
-8
-6
-4
-2
0
2
4
6
8
10
Drift (%)
She
ar S
tress
( √f'c
, [ps
i])
Specimen S9 (RC)Specimen S10 (HPFRC)
214
(a) Specimen S1
(b) Specimen S2
Fig. 4-17 Load versus Drift Envelope Response
-3 -2 -1 0 1 2 3-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Drift (%)
Late
ral F
orce
(kip
s)
first cyclesecond cycle
-3 -2 -1 0 1 2 3-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Drift (%)
Late
ral F
orce
(kip
s)
first cyclesecond cycle
215
(c) Specimen S4
(c) Specimen S5
Fig. 4-17 Load versus Drift Envelope Response
-3 -2 -1 0 1 2 3-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Drift (%)
Late
ral F
orce
(kip
s)
first cyclesecond cycle
-3 -2 -1 0 1 2 3-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Drift (%)
Late
ral F
orce
(kip
s)
first cyclesecond cycle
216
(e) Specimen S6
(f) Specimen S7
Fig. 4-17 Load versus Drift Envelope Response
-3 -2 -1 0 1 2 3-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Drift (%)
Late
ral F
orce
(kip
s)
first cyclesecond cycle
-3 -2 -1 0 1 2 3-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Drift (%)
Late
ral F
orce
(kip
s)
first cyclesecond cycle
217
(g) Specimen S8
(h) Specimen S9
Fig. 4-17 Load versus Drift Envelope Response
-3 -2 -1 0 1 2 3-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Drift (%)
Late
ral F
orce
(kip
s)
first cyclesecond cycle
-3 -2 -1 0 1 2 3-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Drift (%)
Late
ral F
orce
(kip
s)
first cyclesecond cycle
218
(i) Specimen S10
Fig. 4-17 Load versus Drift Envelope Response
-3 -2 -1 0 1 2 3-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Drift (%)
Late
ral F
orce
(kip
s)
first cyclesecond cycle
219
(a) Specimen S2
(b) Specimen S4
Fig. 4-18 Load versus Average Shear Strain Response
-0.03 -0.02 -0.01 0 0.01 0.02 0.03-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Average Shear Strain (rad)
Late
ral F
orce
(kip
s)
-0.03 -0.02 -0.01 0 0.01 0.02 0.03-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Average Shear Strain (rad)
Late
ral F
orce
(kip
s)
1.9% drift
220
(c) Specimen S5
(d) Specimen S6
Fig. 4-18 Load versus Average Shear Strain Response
-0.03 -0.02 -0.01 0 0.01 0.02 0.03-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Average Shear Strain (rad)
Late
ral F
orce
(kip
s)
-0.03 -0.02 -0.01 0 0.01 0.02 0.03-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Average Shear Strain (rad)
Late
ral F
orce
(kip
s)
1.6% drift
221
(e) Specimen S7
(f) Specimen S8
Fig. 4-18 Load versus Average Shear Strain Response
-0.03 -0.02 -0.01 0 0.01 0.02 0.03-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Average Shear Strain (rad)
Late
ral F
orce
(kip
s)
-0.03 -0.02 -0.01 0 0.01 0.02 0.03-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Average Shear Strain (rad)
Late
ral F
orce
(kip
s)
222
(g) Specimen S9
(h) Specimen S10
Fig. 4-18 Load versus Average Shear Strain Response
-0.03 -0.02 -0.01 0 0.01 0.02 0.03-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Average Shear Strain (rad)
Late
ral F
orce
(kip
s)
1.2% drift
-0.03 -0.02 -0.01 0 0.01 0.02 0.03-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Average Shear Strain (rad)
Late
ral F
orce
(kip
s)
223
Fig. 4-19 Comparison of Shear Strain Response Calculated using Diagonal Potentiometers and Optotrak Markers for Specimen S5
-0.03 -0.02 -0.01 0 0.01 0.02 0.03-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Average Shear Strain (rad)
Late
ral F
orce
(kip
s)
diagonal potentiometersoptotrak markers
224
(a) RC Wall Specimens
(b) HPFRC Wall Specimens
Fig. 4-20 Average Shear Strain versus Drift Envelope Response
0 0.5 1 1.5 2 2.5 30
0.005
0.01
0.015
0.02
0.025
0.03
Drift (%)
Ave
rage
She
ar S
train
(rad
)
S4S6S9
0 0.5 1 1.5 2 2.5 30
0.005
0.01
0.015
0.02
0.025
0.03
Drift (%)
Aver
age
Shea
r Stra
in (r
ad)
S2S5S7S8S10
225
Fig. 4-21 Comparison of Shear Strain Response Calculated Using Method 1 (Eq. 4-4) and Method 2 (average of shear strain in strips) (Specimen S4)
-0.03 -0.02 -0.01 0 0.01 0.02 0.03-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Average Shear Strain (rad)
Late
ral F
orce
(kip
s)
Method 1Method 2
226
(a) Specimen S4
(b) Specimen S10
Fig. 4-22 Shear Strain versus Drift Envelope Response at Each Strip (Specimen S10)
0 0.5 1 1.5 2 2.5 30
0.01
0.02
0.03
0.04
0.05
0.06
Drift (%)
She
ar S
train
(rad
)
strip 1strip 2strip 3strip 4strip 5
0 0.5 1 1.5 2 2.5 30
0.01
0.02
0.03
0.04
0.05
0.06
Drift (%)
She
ar S
train
(rad
)
strip 1strip 2strip 3strip 4strip 5
227
(a) Specimen S1
(b) Specimen S6
Fig. 4-23 Load versus Base Slip Response for RC Specimens
-1 -0.5 0 0.5 1-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Slip (in.)
Late
ral F
orce
(kip
s)
0.5% drift
-1 -0.5 0 0.5 1-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Slip (in.)
Late
ral F
orce
(kip
s)
228
(c) Specimen S4
(d) Specimen S9
Fig. 4-23 Load versus Base Slip Response for RC Specimens
-1 -0.5 0 0.5 1-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Slip (in.)
Late
ral F
orce
(kip
s)
-1 -0.5 0 0.5 1-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Slip (in.)
Late
ral F
orce
(kip
s)
229
Fig. 4-24 Load versus Base Slip Response for HPFRC Specimen S2
(a) Specimen S5
Fig. 4-25 Load versus Slip Response at Horizontal Crack for HPFRC Specimens with Dowel Bars at the Base
-1 -0.5 0 0.5 1-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Slip (in.)
Late
ral F
orce
(kip
s)
-1 -0.5 0 0.5 1-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Slip (in.)
Late
ral F
orce
(kip
s)
230
(b) Specimen S10 Fig. 4-25 Load versus Slip Response at Horizontal Crack for HPFRC Specimens
with Dowel Bars at the Base
(a) Specimen S6 Fig. 4-26 Load versus Dilation Response for Specimens with a Shear Span-to-
Length Ratio of 1.5
-1 -0.5 0 0.5 1-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Slip (in.)
Late
ral F
orce
(kip
s)
0 0.05 0.1 0.15 0.2 0.25 0.3-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Dilation (in.)
Late
ral F
orce
(kip
s)
BottomTop
231
(b) Specimen S7
(c) Specimen S8
Fig. 4-26 Load versus Dilation Response for Specimens with a Shear Span-to-Length Ratio of 1.5
0 0.05 0.1 0.15 0.2 0.25 0.3-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Dilation (in.)
Late
ral F
orce
(kip
s)
BottomTop
0 0.05 0.1 0.15 0.2 0.25 0.3-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Dilation (in.)
Late
ral F
orce
(kip
s)
BottomTop
232
Fig. 4-27 Comparison of Dilation at Bottom of Wall for Specimens S9 and S10
(a) Specimen S1
Fig. 4-28 Load versus Concentrated Rotation for Test Specimens
0 0.05 0.1 0.15 0.2 0.25 0.3-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Dilation (in.)
Late
ral F
orce
(kip
s)
Bottom (S9)Bottom (S10)
-0.02 -0.01 0 0.01 0.02-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Rotation (rad)
Late
ral F
orce
(kip
s)
1.0% drift
233
(b) Specimen S2
(c) Specimen S4
Fig. 4-28 Load versus Concentrated Rotation for Test Specimens
-0.02 -0.01 0 0.01 0.02-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120120
Rotation (rad)
Late
ral F
orce
(kip
s)
-0.02 -0.01 0 0.01 0.02-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Rotation (rad)
Late
ral F
orce
(kip
s)
234
(d) Specimen S5
(e) Specimen S6
Fig. 4-28 Load versus Concentrated Rotation for Test Specimens
-0.02 -0.01 0 0.01 0.02-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Rotation (rad)
Late
ral F
orce
(kip
s)
1.4% drift
-0.02 -0.01 0 0.01 0.02-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Drift (%)
Late
ral F
orce
(kip
s)
1.4% drift
235
(f) Specimen S7
(g) Specimen S8
Fig. 4-28 Load versus Concentrated Rotation for Test Specimens
-0.02 -0.01 0 0.01 0.02-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Rotation (rad)
Late
ral F
orce
(kip
s)
-0.02 -0.01 0 0.01 0.02-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Rotation (rad)
Late
ral F
orce
(kip
s)
1.3% drift
236
(h) Specimen S9
(i) Specimen S10
Fig. 4-28 Load versus Concentrated Rotation for Test Specimens
-0.02 -0.01 0 0.01 0.02-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Rotation (rad)
Late
ral F
orce
(kip
s)
1.0% drift
-0.02 -0.01 0 0.01 0.02-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120120
Rotation (rad)
Late
ral F
orce
(kip
s)
237
(a) Specimen S1
(b) Specimen S2
Fig. 4-29 Rotation versus Drift Envelope Response for Wall Specimens
0 0.5 1 1.5 2 2.5 30
0.0025
0.005
0.0075
0.01
0.0125
0.0150.015
Drift (%)
Rot
atio
n (ra
d)
0.1h0.5h0.8h
0 0.5 1 1.5 2 2.5 30
0.0025
0.005
0.0075
0.01
0.0125
0.0150.015
Drift (%)
Rot
atio
n (ra
d)
0.1h0.5h0.8h
238
(c) Specimen S4
(d) Specimen S5
Fig. 4-29 Rotation versus Drift Envelope Response for Wall Specimens
0 0.5 1 1.5 2 2.5 30
0.0025
0.005
0.0075
0.01
0.0125
0.0150.015
Drift (%)
Rot
atio
n (ra
d)
0.1h0.2h0.5h0.7h
0 0.5 1 1.5 2 2.5 30
0.0025
0.005
0.0075
0.01
0.0125
0.015
Drift (%)
Rot
atio
n (ra
d)
0.1h0.2h0.5h0.7h
239
(e) Specimen S6
(f) Specimen S7
Fig. 4-29 Rotation versus Drift Envelope Response for Wall Specimens
0 0.5 1 1.5 2 2.5 30
0.0025
0.005
0.0075
0.01
0.0125
0.015
Drift (%)
Rot
atio
n (ra
d)
0.1h0.6h0.9h
0 0.5 1 1.5 2 2.5 30
0.0025
0.005
0.0075
0.01
0.0125
0.0150.015
Drift (%)
Rot
atio
n (ra
d)
0.1h0.6h0.9h
instrumentation stopped working
240
(g) Specimen S8
(h) Specimen S9
Fig. 4-29 Rotation versus Drift Envelope Response for Wall Specimens
0 0.5 1 1.5 2 2.5 30
0.0025
0.005
0.0075
0.01
0.0125
0.0150.015
Drift (%)
Rot
atio
n (ra
d)
0.1h0.6h0.9h
0 0.5 1 1.5 2 2.5 30
0.0025
0.005
0.0075
0.01
0.0125
0.0150.015
Drift (%)
Rot
atio
n (ra
d)
0.1h0.2h0.35h0.55h
241
(i) Specimen S10
Fig. 4-29 Rotation versus Drift Envelope Response for Wall Specimens
Fig. 4-30 Load versus Strain Response in Longitudinal Bar of Wall Boundary Element in Specimen S1
0 0.5 1 1.5 2 2.5 30
0.0025
0.005
0.0075
0.01
0.0125
0.0150.015
Drift (%)
Rot
atio
n (ra
d)
0.1h0.2h0.35h0.55h
-0.02 -0.01 0 0.01 0.02-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Strain
Late
ral F
orce
(kip
s)
V1 (at wall base)V5 (at 0.5h)
242
Fig. 4-31 Load versus Strain Response in a Horizontal Bar of Specimen S1
Fig. 4-32 Load versus Strain Response in a Vertical Bar of Specimen S4
-0.02 -0.01 0 0.01 0.02-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Strain
Late
ral F
orce
(kip
s)
H4 (at 0.1h)
-0.02 -0.01 0 0.01 0.02-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Strain
Late
ral F
orce
(kip
s)
V2-2 (at 0.25h)
243
Fig. 4-33 Load versus Strain Response in a Horizontal Bars of Specimens S4 and S5
Fig. 4-34 Load versus Strain Response in Longitudinal Bar of Wall Boundary Element in Specimen S6
-0.02 -0.01 0 0.01 0.02-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Strain
Late
ral F
orce
(kip
s)
S4 (H4-1)S5 (H5-1)
-0.02 -0.01 0 0.01 0.02-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Strain
Late
ral F
orce
(kip
s)
V19 (at 0.5h)
244
Fig. 4-35 Load versus Strain Response in Horizontal Bars of Specimen S6
Fig. 4-36 Load versus Strain Response in Horizontal Bars at 0.3h for Specimens S9 and S10
-0.02 -0.01 0 0.01 0.02-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Strain
Late
ral F
orce
(kip
s)
H6 (0.25h)H10 (0.5h)
-0.02 -0.01 0 0.01 0.02-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
Strain
Late
ral F
orce
(kip
s)
S9 (H3-1)S10 (H3-2)
245
(a) RC Specimens
(b) HPFRC Specimens
Fig. 4-37 Drift versus Strain in Main Longitudinal Bars at 1 in. from Wall Base
0 0.5 1 1.5 2 2.5 30
0.005
0.01
0.015
0.02
0.025
0.03
Drift (%)
Stra
in
S1S4S6S9
0 0.5 1 1.5 2 2.5 30
0.005
0.01
0.015
0.02
0.025
0.03
Drift (%)
Stra
in
S2S5S8S10
246
(a) RC Specimens
(b) HPFRC Specimens
Fig. 4-38 Drift versus Strain in Main Longitudinal Bars at Wall Mid-Height
0 0.5 1 1.5 2 2.5 30
0.005
0.01
0.015
0.02
0.025
0.03
Drift (%)
Stra
in
S1S4S6S9
0 0.5 1 1.5 2 2.5 30
0.005
0.01
0.015
0.02
0.025
0.03
Drift (%)
Stra
in
S2S5S7S8S10
247
Fig. 4-39 Drift versus Strain in Dowel Bars at 1 in. from Wall Base in HPFRC Specimens
(a) RC Specimens
Fig. 4-40 Drift versus Strain at a Horizontal Bar at a Height of 0.1h
0 0.5 1 1.5 2 2.5 30
0.005
0.01
0.015
0.02
0.025
0.03
Drift (%)
Stra
in
S5S7S8S10
0 0.5 1 1.5 2 2.5 30
0.005
0.01
0.015
0.02
0.025
0.03
Drift (%)
Stra
in
S1 (5.9√f'c, psi)S4 (8.0√f'c,psi)S6 (6.7√f'c, psi)S9 (9.4√f'c, psi)
248
(b) HPFRC Specimens
Fig. 4-40 Drift versus Strain at a Horizontal Bar at a Height of 0.1h
Fig. 4-41 Drift versus Strain at a Horizontal Bar at a Height of 0.25h
0 0.5 1 1.5 2 2.5 30
0.005
0.01
0.015
0.02
0.025
0.03
Drift (%)
Stra
in
S2 (4.4√f'c, psi)S5 (6.4√f'c, psi)S8 (6.5√f'c, psi)S10 (8.9√f'c, psi)
0 0.5 1 1.5 2 2.5 30
0.005
0.01
0.015
0.02
0.025
0.03
Drift (%)
Stra
in
S4 (8.0√f'c), psiS5 (6.4√f'c), psiS9 (9.4√f'c), psiS10 (8.9√f'c), psi
249
(a) RC Specimens
(b) HPFRC Specimens
Fig. 4-42 Drift versus Strain at a Horizontal Bar at a Height of 0.5h
0 0.5 1 1.5 2 2.5 30
0.005
0.01
0.015
0.02
0.025
0.03
Drift (%)
Stra
in
S1 (5.9√f'c, psi)S4 (8.0√f'c, psi)S6 (6.7√f'c, psi)S9 (9.4√f'c, psi)
0 0.5 1 1.5 2 2.5 30
0.005
0.01
0.015
0.02
0.025
0.03
Drift (%)
Stra
in
S2 (4.4√f'c, psi)S5 (6.4√f'c, psi)S8 (6.5√f'c, psi)S10 (8.9√f'c, psi)
250
(a) Specimens S1 and S2
(b) Specimens S4 and S5
Fig. 4-43 Normalized Peak-to Peak Stiffness versus Drift for Wall Specimens
0 0.5 1 1.5 2 2.5 30
10
20
30
40
50
60
70
80
90
100
Drift (%)
Nor
mal
ized
Stif
fnes
s (%
)
S1 (RC)S2 (HPFRC)
solid line = first cycledashed line = second cycle
0 0.5 1 1.5 2 2.5 30
10
20
30
40
50
60
70
80
90
100
Drift (%)
Nor
mal
ized
Stif
fnes
s (%
)
S4 (RC)S5 (HPFRC)
solid line = first cycledashed line = second cycle
251
(c) Specimens S6 and S7
(d) Specimens S9 and S10
Fig. 4-43 Normalized Peak-to Peak Stiffness versus Drift for Wall Specimens
0 0.5 1 1.5 2 2.5 30
10
20
30
40
50
60
70
80
90
100
Drift (%)
Nor
mal
ized
Stif
fnes
s (%
)
S6 (RC)S7 (HPFRC)
solid line = first cycledashed line = second cycle
0 0.5 1 1.5 2 2.5 30
10
20
30
40
50
60
70
80
90
100
Drift (%)
Nor
mal
ized
Stif
fnes
s (%
)
S9 (RC)S10 (HPFRC)
solid line = first cycledashed line = second cycle
252
Fig.4-44 Comparison of Normalized Stiffness for RC Wall Specimens
Fig.4-45 Comparison of Normalized Stiffness for HPFRC Wall Specimens
0 0.5 1 1.5 2 2.5 30
10
20
30
40
50
60
70
80
90
100
Drift (%)
Nor
mal
ized
Stif
fnes
s (%
)
S1 (5.9√f'c)S4 (8.0√f'c)S6 (6.7√f'c)S9 (9.4√f'c)
0 0.5 1 1.5 2 2.5 30
10
20
30
40
50
60
70
80
90
100
Drift (%)
Nor
mal
ized
Stif
fnes
s (%
)
S2 (4.4√f'c)S5 (6.4√f'c)S7 (6.2√(f'c)S10 (8.6√f'c)
253
(a) Specimens with
(b) Specimens with
Fig. 4-46 Energy Dissipated versus Drift for Wall Specimens
0 0.5 1 1.5 2 2.5 30
25
50
75
100
125
150150
Drift (%)
Ene
rgy
Dis
sipa
ted
(kip
-in.)
S1 (RC)S2 (HPFRC)S4 (RC)S5 (HPFRC)
solid line = first cycledashed line = second cycle
0 0.5 1 1.5 2 2.5 30
25
50
75
100
125
150150
Drift (%)
Ene
rgy
Dis
sipa
ted
(kip
-in.)
S6 (RC)S7 (HPFRC)S8 (HPFRC)S9 (RC)S10 (HPFRC)
solid line = first cycledashed line = second cycle
254
(a) Specimens with
(b) Specimens with
Fig. 4-47 Normalized Energy Dissipated versus Drift for Wall Specimens
0 0.5 1 1.5 2 2.5 30
10
20
30
40
50
60
Drift (%)
Nom
raliz
ed E
nerg
y D
issi
pate
d (%
)
S1 (RC)S2 (HPFRC)S4 (RC)S5 (HPFRC)
solid line = first cycledashed line = second line
0 0.5 1 1.5 2 2.5 30
10
20
30
40
50
60
Drift (%)
Nom
raliz
ed E
nerg
y D
issi
pate
d (%
)
S6 (RC)S7 (HPFRC)S8 (HPFRC)S9 (RC)S10 (HPFRC)
solid line = first cycledashed line = second cycle
255
Fig. 5-1 Definition of Shear Strain for the Calculation of Wall Deformation Components
wall slip
256
Fig. 5-2 Calculation of Curvature over the Wall Height
257
(a) RC Specimen S4
(b) RC Specimen S9
Fig. 5-3 Contribution of Deformation Components to Drift
0 0.5 1 1.5 2 2.5 30
20
40
60
80
100
120
Drift (%)
Con
tribu
tion
to D
rift (
%)
rotation
shear distortion
slip
0 0.5 1 1.5 2 2.5 30
20
40
60
80
100
120
Drift (%)
Con
tribu
tion
to D
rift (
%)
rotation
shear distortion
slip
258
(c) HPFRC Specimen S5
(d) HPFRC Specimen S10
Fig. 5-3 Contribution of Deformation Components to Drift
0 0.5 1 1.5 2 2.5 30
20
40
60
80
100
120
Drift (%)
Con
tribu
tion
to D
rift (
%)
rotation
shear distortion
slip
0 0.5 1 1.5 2 2.5 30
20
40
60
80
100
120
Drift (%)
Con
tribu
tion
to D
rift (
%)
rotation
shear distortion
slip
259
(a) Positive loading direction
b) Negative loading direction
Fig. 5-4 Curvature Distribution for RC Specimen S4
0 0.5 1 1.5 2x 10-3
0
5
10
15
20
25
30
35
Curvature (rad/in.)
Hei
ght (
in.)
0.25% drift0.35% drift0.45% drift0.55% drift
theoretical yield curvature
0 0.5 1 1.5 2x 10-3
0
5
10
15
20
25
30
35
Curvature (rad/in.)
Hei
ght (
in.)
0.75% drift1.0% drift1.3% drift1.5% drift
theoretical yield curvature
0 0.5 1 1.5 2x 10-3
0
5
10
15
20
25
30
35
Curvature (rad/in.)
Hei
ght (
in.)
-0.20% drift-0.35% drift-0.55% drift
theoretical yield curvature
0 0.5 1 1.5 2x 10-3
0
5
10
15
20
25
30
35
Curvature (rad/in.)
Hei
ght (
in.)
-0.90% drift-1.0% drift-1.3% drift
theoretical yield curvature
260
a) Positive loading direction
Fig. 5-5 Curvature Distribution for HPFRC Specimen S5
0 0.5 1 1.5 2x 10-3
0
5
10
15
20
25
30
35
Curvature (rad/in.)
Hei
ght (
in.)
0.10% drift0.25% drift0.35% drift0.50% drift
theoretical yield curvature
0 0.5 1 1.5 2x 10-3
0
5
10
15
20
25
30
35
Curvature (rad/in)
Hei
ght (
in.)
0.65% drift0.85% drift1.1% drift1.4% drift
theoretical yield curvature
0 0.5 1 1.5 2x 10-3
0
5
10
15
20
25
30
35
Curvature (rad/in.)
Hei
ght (
in.)
1.6% drift1.9% drift2.3% drift
theoretical yield curvature
261
b) Negative loading direction
Fig. 5-5 Curvature Distribution for HPFRC Specimen S5
0 0.5 1 1.5 2x 10-3
0
5
10
15
20
25
30
35
Curvature (rad/in.)
Hei
ght (
in.)
-0.15% drift-0.30% drift-0.45% drift
theoretical yield curvature
0 0.5 1 1.5 2x 10-3
0
5
10
15
20
25
30
35
Curvature (rad/in.)
Hei
ght (
in.)
-0.60% drift-0.80% drift-1.1% drift-1.4% drift
theoretical yield curvature
0 0.5 1 1.5 2x 10-3
0
5
10
15
20
25
30
35
Curvature (rad/in.)
Hei
ght (
in.)
-1.7% drift-2.0% drift-2.4% drift
theoretical yield curvature
262
a) Positive loading direction
Fig. 5-6 Curvature Distribution for RC Specimen S9
0 0.5 1 1.5 2x 10-3
0
5
10
15
20
25
30
35
Curvature (rad/in.)
Hei
ght (
in.)
0.10% drift0.20% drift0.30% drift
theoretical yield curvature
0 0.5 1 1.5 2x 10-3
0
5
10
15
20
25
30
35
Curvature (rad/in)
Hei
ght (
in)
0.70%0.90%1.30%1.50%
theoretical yield curvature
0 0.5 1 1.5 2x 10-3
0
5
10
15
20
25
30
35
Curvature (rad/in.)
Hei
ght (
in.)
1.9% drift
theoretical yield curvature
263
b) Negative loading direction
Fig. 5-6 Curvature Distribution for RC Specimen S9
0 0.5 1 1.5 2x 10-3
0
5
10
15
20
25
30
35
Curvature (rad/in.)
Hei
ght (
in.)
-0.10% drift-0.20% drift-0.30% drift-0.50% drift
theoretical yield curvature
0 0.5 1 1.5 2x 10-3
0
5
10
15
20
25
30
35
Curvature (rad/in.)
Hei
ght (
in.)
-0.70% drift-1.0% drift1.2% drift-1.5% drift
theoretical yield curvature
0 0.5 1 1.5 2x 10-3
0
5
10
15
20
25
30
35
Curvature (rad/in.)
Hei
ght (
in.)
-1.8% drift-2.1% drift
theoretical yield curvature
264
a) Positive loading direction
Fig. 5-7 Curvature Distribution for HPFRC Specimen S10
0 0.5 1 1.5 2x 10-3
0
5
10
15
20
25
30
35
Curvature (rad/in.)
Hei
ght (
in.)
0.20% drift0.30% drift0.40% drift
theoretical yield curvature
0 0.5 1 1.5 2x 10-3
0
5
10
15
20
25
30
35
Curvature (rad/in.)
Hei
ght (
in.)
0.65% drift0.80% drift1.2% drift1.2% drift1.5% drift
theoretical yield curvature
0 0.5 1 1.5 2x 10-3
0
5
10
15
20
25
30
35
Curvature (rad/in.)
Hei
ght (
in.)
1.8% drift2.1% drift2.4% drift
theoretical yield curvature
265
b) Negative loading direction
Fig. 5-7 Curvature Distribution for HPFRC Specimen S10
0 0.5 1 1.5 2x 10-3
0
5
10
15
20
25
30
35
Curvature (rad/in.)
Hei
ght (
in.)
-0.15% drift-0.25% drift-0.35% drift-0.45% drift
theoretical yield curvature
0 0.5 1 1.5 2x 10-3
0
5
10
15
20
25
30
35
Curvature (rad/in.)
Hei
ght (
in.)
-0.60% drift-0.90% drift-1.0% drift-1.3% drift
theoretica yield curvaturel
0 0.5 1 1.5 2x 10-3
0
5
10
15
20
25
30
35
Curvature (rad/in.)
Hei
ght (
in.)
-1.6% drift-1.9% drift-2.1% drift
theoretical yield curvature
266
Stress
Strain
Stress
*
Fig. 5-8 Tensile Stress-Strain Model for HPFRC Matrix
Effective Strain
Fig. 5-9 Compression Stress-Strain Model for Regular Concrete and HPFRC Matrix
Crack opening Strain Strain
267
Stress
Strain
Fig. 5-10 Tensile Stress-Strain Model for Steel Reinforcement
268
Fig. 5-11 Moment versus Curvature Response for RC Specimen S4
0 0.2 0.4 0.6 0.8 1 1.2 1.4
x 10-3
0
1000
2000
3000
4000
5000
6000
7000
Curvature (rad/in.)
Mom
ent (
kip-
in.)
experimental-wall base
experimental-4 in. above wall base
nonlinear analysis
1.7% drift
269
Fig. 5-12 Moment versus Curvature Response for HPFRC Specimen S5
0 0.2 0.4 0.6 0.8 1 1.2 1.4
x 10-3
0
1000
2000
3000
4000
5000
6000
7000
Curvature (rad/in.)
Mom
ent (
kip-
in.)
experimental-wall baseexperimental-4 in. above wall basenonlinear analysis-wall basenonlinear analysis-end line of dowelsnonlinear analysis-end line of dowels w/o FRC
2.0% drift
270
Fig. 5-13 Moment versus Curvature Response for RC Specimen S9
0 0.2 0.4 0.6 0.8 1 1.2 1.4
x 10-3
0
1000
2000
3000
4000
5000
6000
7000
Curvature (rad/in.)
Mom
ent (
kip-
in.)
experimental-wall baseexperimental-4 in. above wall basenonlinear analysis
1.8% drift
271
Fig. 5-14 Moment versus Curvature Response for HPFRC Specimen S10
0 0.2 0.4 0.6 0.8 1 1.2 1.4
x 10-3
0
1000
2000
3000
4000
5000
6000
7000
Curvature (rad/in.)
Mom
ent (
kip-
in.)
experimental-wall baseexperimental-4 in. above wall basenonlinear analysis-wall basenonlinear analysis-end line of dowelsnonlinear analysis-end line of dowels w/o FRC
2.5% drift
1.6% drift
272
Fig. 5-15 Ratio of Measured Shear Strength to Shear Strength Calculated Using the Shear Friction Analogy versus Shear Friction Strength
Fig. 5-16 Measured Shear Strength versus Shear Friction Capacity
0 500 1000 1500 2000 2500 30000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
(Avffy)/Acv (psi)
v max
/vns
f
RC SpecimensHPFRC Specimens
0 500 1000 1500 2000 2500 30000
100
200
300
400
500
600
700
800
900
1000
(Avffy)/Acv (psi)
v max
(psi
)
RC SpecimensHPFRC Specimens
y = 0.27 x +180
273
Fig. 5-17 Measured Normalized Shear Strength versus Shear Friction Strength
Fig. 5-18 Shear Force Normalized by Shear Friction Strength versus Horizontal Sliding Envelope Response
0 500 1000 1500 2000 2500 30000
1
2
3
4
5
6
7
8
9
10
(Avffy)/Acv (psi)
v max
( √f' c,[p
si])
RC SpecimensHPFRC Specimens
Specimen S2
0 0.1 0.2 0.3 0.4 0.5 0.60
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Sliding at Horizontal Crack (in.)
V/(A
vff yµ
)
θ = 0.15%θ = 0.25%θ = 0.35%θ = 0.45%
S1 S5
S6 S9
S10
274
Fig. 5-19 Shear Force Normalized by Shear Friction Strength versus Horizontal Sliding Envelope Response for HPFRC Specimens S5 and S10 at the
Wall Base (Cold Joint)
0 0.1 0.2 0.3 0.4 0.5 0.60
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Sliding at Wall Base (in.)
V/(A
vff yµ
) S10
S5
275
Fig. 5-20 Sliding Stiffness versus Average Horizontal Crack Width
Fig. 5-21 Sliding Stiffness Normalized by Shear Friction Capacity versus Average Horizontal Crack Width
0 0.05 0.1 0.15 0.20
50
100
150
200
250
300
Average crack width at horizontal crack (in.)
Slid
ing
Stif
fnes
s, K
s (ksi
/in.)
S5-positive loadingS5-negative loadingS10-positive loadingS10-negative loading
0 0.05 0.1 0.15 0.20
0.25
0.5
0.75
1
1.25
1.51.5
Average crack width at horizontal crack (in.)
Ks /
Vns
f (1/
in.)
S5-positive loadingS5-negative loadingS10-positive loadingS10-negative loading
276
a) Positive Loading Direction
Fig. 5-22 Sliding Stiffness and Slip versus Crack Width on Tension Face of Horizontal Crack for HPFRC Specimen S5
0 0.05 0.1 0.15 0.2 0.25 0.30
50
100
150
200S
lidin
g S
tiffn
ess,
Ks (k
si/in
.)
Crack width at tension face (in.)0 0.05 0.1 0.15 0.2 0.25 0.3
0
0.2
0.4
0.6
0.8
Slip
(in.
)
277
b) Negative Loading Direction
Fig. 5-22 Sliding Stiffness and Slip versus Crack Width on Tension Face of Horizontal Crack for HPFRC Specimen S5
0 0.05 0.1 0.15 0.2 0.25 0.30
50
100
150
200S
lidin
g S
tiffn
ess,
Ks (k
si/in
.)
Crack width at tension face (in.)0 0.05 0.1 0.15 0.2 0.25 0.3
0
0.2
0.4
0.6
0.8
Slip
(in.
)
278
a) Positive Loading Direction
Fig. 5-23 Sliding Stiffness and Slip versus Crack Width on Tension Face of Horizontal Crack for HPFRC Specimen S10
0 0.05 0.1 0.15 0.2 0.25 0.30
50
100
150
200S
lidin
g S
tiffn
ess,
Ks (k
si/in
.)
Crack width at tension face (in.)0 0.05 0.1 0.15 0.2 0.25 0.3
0
0.2
0.4
0.6
0.8
Slip
(in.
)
279
b) Negative Loading Direction
Fig. 5-23 Sliding Stiffness and Slip versus Crack Width on Tension Face of Horizontal Crack for HPFRC Specimen S10
0 0.05 0.1 0.15 0.2 0.25 0.30
50
100
150
200S
lidin
g S
tiffn
ess,
Ks (k
si/in
.)
Crack width at tension face (in.)0 0.05 0.1 0.15 0.2 0.25 0.3
0
0.2
0.4
0.6
0.8
Slip
(in.
)
280
a) HPFRC Specimen S7
b) HPFRC Specimen S8
Fig. 5-24 Shear Stress versus Shear Distortion in HPFRC Specimens S7 and S8
-0.03 -0.02 -0.01 0 0.01 0.02 0.030
1
2
3
4
5
6
7
8
Shear Distortion γ (rad)
She
ar S
tress
(√f
'c, [
psi])
positive loading directionnegative loading direction
-0.03 -0.02 -0.01 0 0.01 0.02 0.030
1
2
3
4
5
6
7
8
Shear Distortion γ (rad)
She
ar S
tress
( √f'c
, [ps
i])
positve loading directionnegative loading direction
281
a) HPFRC Specimen S7
b) HPFRC Specimen S8
Fig. 5-25 Shear Strain to Rotation Ratio versus Shear Stress for Specimens S7 and S8
0 2 4 6 80
0.5
1
1.5
2
2.5
3
3.5
4
Shear Stress (√f'c, [psi])
Rat
io γ
/ θ
positive loading directionnegative loading direction
0 2 4 6 80
0.5
1
1.5
2
2.5
3
3.5
4
Shear Stress (√f'c, [psi])
Rat
io γ
/ θ
positive loading directionnegative loading direction
282
Fig. 5-26 Peak Shear Stress versus Drift Capacity for Test Specimens in this Study
0 1 2 3 40
1
2
3
4
5
6
7
8
9
1010
Drift Capacity (%)
She
ar S
tress
( √f' c, [
psi])
RC Specimens (α/lw=1.2)
RC Specimens (α/lw=1.5)
HPFRC Specimens (α/lw=1.2)
HPFRC Specimens (α/lw=1.5)
283
Note: Specimen SW13 (Cardenas et al., 1980) and all HPFRC walls in this study were tested under reversed cyclic loading. All other specimens were tested under monotonic loading.
Fig. 5-27 Comparison of Peak Shear Stress versus Drift Capacity for Walls with No or Little Confinement Reinforcement in the Boundary Regions
0 1 2 3 40
1
2
3
4
5
6
7
8
9
10
Drift Capacity (%)
She
ar S
tress
( √f' c, [
psi])
Cardenas et al. (1980)Maier (1999)This study (HPFRC walls)
SW13
284
Fig. 5-28 Peak Shear Stress versus Drift Capacity versus for Wall Specimens with Various Confinement Reinforcing Ratios
0 1 2 3 40
1
2
3
4
5
6
7
8
9
10
Drift Capacity (%)
She
ar S
tress
( √f' c, [
psi])
RC-no confinementRC-0.67% confinementRC-1.0% confinementRC-1.7% confinementHPFRC-no confinementHPFRC-0.25% confinement
Solid markers: monotonic loadingHollow markers: reversed cyclic loading
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